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Geosci. Model Dev., 8, 2465–2513, 2015
www.geosci-model-dev.net/8/2465/2015/
doi:10.5194/gmd-8-2465-2015
© Author(s) 2015. CC Attribution 3.0 License.
PISCES-v2: an ocean biogeochemical model for carbon and
ecosystem studies
O. Aumont1 , C. Ethé2 , A. Tagliabue3 , L. Bopp4 , and M. Gehlen4
1 Laboratoire
d’Océanographie et de Climatologie: Expérimentation et Approches Numériques, IPSL, 4 Place Jussieu,
75005 Paris, France
2 Institut Pierre et Simon Laplace, 4 Place Jussieu, 75005 Paris, France
3 Dept. of Earth, Ocean and Ecological Sciences, School of Environmental Sciences, University of Liverpool,
4 Brownlow Street, Liverpool L69 3GP, UK
4 Laboratoire des Sciences du Climat et de l’Environement, IPSL, Orme des Merisiers, 91190 Gif-sur-Yvette, France
Correspondence to: O. Aumont ([email protected])
Received: 11 December 2014 – Published in Geosci. Model Dev. Discuss.: 16 February 2015
Revised: 29 June 2015 – Accepted: 4 July 2015 – Published: 13 August 2015
Abstract. PISCES-v2 (Pelagic Interactions Scheme for Carbon and Ecosystem Studies volume 2) is a biogeochemical
model which simulates the lower trophic levels of marine
ecosystems (phytoplankton, microzooplankton and mesozooplankton) and the biogeochemical cycles of carbon and of
the main nutrients (P, N, Fe, and Si). The model is intended
to be used for both regional and global configurations at high
or low spatial resolutions as well as for short-term (seasonal,
interannual) and long-term (climate change, paleoceanography) analyses. There are 24 prognostic variables (tracers)
including two phytoplankton compartments (diatoms and
nanophytoplankton), two zooplankton size classes (microzooplankton and mesozooplankton) and a description of the
carbonate chemistry. Formulations in PISCES-v2 are based
on a mixed Monod–quota formalism. On the one hand, stoichiometry of C / N / P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and
Si. On the other hand, the iron and silicon quotas are variable and the growth rate of phytoplankton is limited by the
internal availability in Fe. Various parameterizations can be
activated in PISCES-v2, setting, for instance, the complexity of iron chemistry or the description of particulate organic
materials. So far, PISCES-v2 has been coupled to the Nucleus for European Modelling of the Ocean (NEMO) and Regional Ocean Modeling System (ROMS) systems. A full description of PISCES-v2 and of its optional functionalities is
provided here. The results of a quasi-steady-state simulation
are presented and evaluated against diverse observational and
satellite-derived data. Finally, some of the new functionalities of PISCES-v2 are tested in a series of sensitivity experiments.
1
Introduction
Human activities have released large amounts of carbon into
the atmosphere since the beginning of the industrial era
leading to an increase in atmospheric CO2 by more than
100 ppmv. The oceans play a major role in the carbon cycle and in its adjustment. Sabine et al. (2004) have estimated
that the oceans have absorbed about one-third of the anthropogenic emissions. This role is tightly controlled by the physical and biogeochemical states of the marine system, i.e.,
by the characteristics of the solubility and biological pumps.
Yet, the role played by the ocean in the carbon cycle is likely
to be modified in response to climate and chemical changes
induced by the anthropogenic carbon emissions (e.g., Orr
et al., 2005; Steinacher et al., 2010; Bopp et al., 2013). Global
ocean biogeochemical models represent powerful tools to
study the carbon cycle and to predict its response to future
and past climate and chemical changes. Since the pioneering work by Bacastow and Maier-Reimer (1990) based on
a very simple description of the carbon cycle, the number
and the complexity of models have rapidly increased (e.g.,
Six and Maier-Reimer, 1996; Moore et al., 2004; Quéré et al.,
2005; Aumont and Bopp, 2006; Yool et al., 2011). However,
Published by Copernicus Publications on behalf of the European Geosciences Union.
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a greater complexity of the models raises difficulties related
to the lack of data for validation and to the theoretical justification of the parameterizations (e.g., Anderson, 2005, 2010).
PISCES (Pelagic Interactions Scheme for Carbon and
Ecosystem Studies) is a biogeochemical model which simulates marine biological productivity and describes the biogeochemical cycles of carbon and of the main nutrients (P, N,
Si, Fe). This model can be seen as one of the many Monod
models (Monod, 1942) as opposed to the quota models (McCarthy, 1980; Droop, 1983) which are alternative types of
ocean biogeochemical models. Thus, it assumes a constant
Redfield ratio, and phytoplankton growth depends on the external concentration in nutrients. This choice was dictated by
the computing cost whereby the internal pools of the different elements (necessary for a quota model) requires many
more prognostic variables. Ultimately, PISCES was assumed
to be suited for a wide range of spatial and temporal scales,
including, typically, several thousand year-long simulations
on the global scale.
In contrast to the Monod approach, when modeling silicate, iron and/or chlorophyll, assuming constant ratios is not
justified anymore as these ratios can vary substantially. For
instance, the Fe / C ratio can vary by at least an order of
magnitude, in particular as a result of luxury uptake, (e.g.,
Sunda and Huntsman, 1995, 1997) compared to the N / C ratio which varies by “only” 2 to 3 times. Equally, the Si / C
ratio can vary significantly in response to the degree of iron
stress (Hutchins and Bruland, 1998; Takeda, 1998). Thus, in
PISCES, a compromise between the two classical types of
ocean models was chosen. The Fe / C, Si / C and Chl / C internal ratios are prognostically predicted based on the external concentrations of the limiting nutrients as in the quota
approach. Phytoplankton growth rates are predicted simultaneously using the Monod approach for N, P and Si and the
quota approach for Fe. As a consequence, PISCES should be
considered to be a mixed Monod–quota model.
Historically, the development of PISCES started in 1997
with the release of the P3ZD model which was a simple Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD)
model with semi-labile dissolved organic matter (DOM)
(Aumont, 1998; Aumont et al., 2002). Phytoplankton growth
rate was only limited by one nutrient (effectively phosphate)
and many shortcomings were apparent in this model, especially in the high nutrient-low chlorophyll (HNLC) regions.
This served to justify the development, beginning in 1999,
of a more complex model that includes three limiting nutrients (Fe, Si, P), two phytoplankton and two zooplankton size
classes. This model was called HAMOCC5 (Aumont et al.,
2003), as it was based on HAMOCC3.1 (Six and MaierReimer, 1996) and used in the LSG model (Maier-Reimer
et al., 1993). When this code was embedded in the ocean
model Ocean PArallélisé (OPA) (Madec et al., 1998), it required some major changes and improvements, partly because of the much finer vertical resolution. In addition to
the numerical schemes, these changes were mostly an imGeosci. Model Dev., 8, 2465–2513, 2015
O. Aumont et al.: A description of PISCES-v2
proved treatment of the optics and the separation of the particulate organic matter into two different size classes. All
these changes and the major recodings it required led us to
adopt a new name for the model: PISCES. This name can be
translated as fishes from Latin.
PISCES has been used so far to address a wide range
of scientific questions. Unfortunately, a complete list of the
studies which have been based on or made use of PISCES is
not available, but more than about hundred referenced studies explicitly rely directly or indirectly on this model. These
range from process studies (Aumont and Bopp, 2006; Gehlen
et al., 2006; Tagliabue et al., 2009a; Tagliabue and Völker,
2011) to operational oceanography (Brasseur et al., 2009).
PISCES has been used to analyze intraseasonal (Gorgues
et al., 2005; Resplandy et al., 2009) to interannual and
decadal timescales (Raynaud et al., 2006; Rodgers et al.,
2008). PISCES is part of the Institut Pierre et Simon Laplace
(IPSL) and CEntre National de Recherche en Météorologie
(CNRM) Earth system models which contribute to the different Intergovernmental Panel on Climate Change (IPCC)related activities including the Climate Model Intercomparison Project (CMIP5) modeling component (Séférian et al.,
2013). Several studies have been conducted that consider the
potential impact of climate change on ocean biogeochemistry
(Dufresne et al., 2002; Bopp et al., 2005; Steinacher et al.,
2010). Modeling studies focusing on paleoceanography have
been based on PISCES (Bopp et al., 2003; Tagliabue et al.,
2009b). Finally, PISCES is also used in regional configurations to study specific regions such as the Peru upwelling
(Echevin et al., 2008; Albert et al., 2010) or the Indian Ocean
(Resplandy et al., 2012).
PISCES is currently embedded into two modeling systems: NEMO (Madec, 2008) and ROMS_AGRIF (Penven
et al., 2006; Debreu et al., 2011). It can be downloaded from
their respective web sites:
– http://www.nemo-ocean.eu for the NEMO ocean modeling framework;
– http://www.romsagrif.org for the ROMS_AGRIF modeling framework.
However, PISCES-v2 is currently available only in the
NEMO modeling system. The implementation of this updated version of PISCES in the ROMS_AGRIF modeling
system is currently underway and should be finished and
available by the end of 2015.
Since 2001, PISCES has undergone active developments.
In 2004, a stable release of the model was made available to
the community on the OPA web site. Soon after, an earlier
documentation of the model was published as a Supplement
to the study by Aumont and Bopp (2006). Since then, the
model has significantly evolved without any update of the
documentation and this has effectively rendered the earlier
documentation obsolete. After 6 years of intense developments, it is more than appropriate at this point to provide
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O. Aumont et al.: A description of PISCES-v2
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the current or future users of the model with an updated and
accurate description of the current state of PISCES, called
PISCES-v2. This paper describes the main aspects of the
model. At its end, a description of a climatological simulation is proposed using the standard set of parameters available when the model is downloaded. Finally, the impact of
several new parameterizations is evaluated through the performance of a set of sensitivity experiments.
2
d. The relationship between growth rate (primary production) and light can be chosen between two different formulations.
– Changes made to the zooplankton compartments:
a. The microzooplankton grazing formulation is now
identical to that of mesozooplankton.
b. Thresholds can be selected for both total food or
individual prey types.
Changes from previous release
c. Food quality affects the gross growth efficiency of
both zooplankton compartments.
As already mentioned, PISCES as a research tool is in perpetual evolution. Numerous changes have been made relative
to the previously documented version, PISCES-v1. A brief
list of the main changes is made below, with these changes
organized thematically. These changes are detailed in the following sections.
– Changes made to dissolved organic matter and particulate materials:
a. Two different schemes for the description of particulate organic matter can be chosen: the traditional
two-compartment model or the Kriest model.
– Changes made to the code structure and design:
b. Bacterial implicit description has been redesigned.
a. Transition to full native Fortran 90 coding. The
model has also undergone a reorganization of its
architecture and coding conventions following the
evolution of NEMO.
c. Dissolution of biogenic silica assumes two different
fractions.
d. The dust distribution in the water column is modeled using a very crude parameterization.
b. I/O interface should now be set by default to IOM
(the new input–output manager of the NEMO modeling system) to benefit from the major improvements this interface offers.
e. The numerics of vertical sedimentation have been
improved (time splitting scheme).
– Changes made to the external sources of nutrients and
to the treatment of the bottom of the water column:
c. Memory and performance improvements have been
made. This version should run slightly faster and
take much less memory than v1.
a. Spatially variable solubility of iron in dust can be
specified from a file.
d. The namelist now includes many more parameters
that may thus be changed without recompiling the
code.
b. River discharge of nutrients has been improved.
c. Denitrification in sediments is now parameterized
as well as variable preservation of calcite.
– Changes made to the nutrients:
a. iron chemistry can be described according to two
different parameterizations: the simple old chemistry scheme based on one ligand and one inorganic species, and a new complex chemistry module based on five iron species and two ligands.
b. Scavenging of inorganic iron and coagulation of
iron colloids have been redesigned.
– Changes made to the phytoplankton compartments:
a. Nutrients limitation terms now include a simple description of the impact of cell size.
b. Iron content and growth rate limitation by iron is
modeled following the quota formalism. Luxury
uptake of iron can be represented by this new formulation.
c. Silicification, calcification as well as nitrogen fixation are redesigned by diazotrophs.
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As a consequence of these changes, the user should be
warned that results produced with PISCES-v1 cannot be reproduced by PISCES-v2. Furthermore, in the rest of this
work, PISCES will designate PISCES-v2.
3
Model description
PISCES currently has 24 compartments (see Fig. 1). There
are five modeled limiting nutrients for phytoplankton growth:
nitrate and ammonium, phosphate, silicate and iron. It should
be mentioned that phosphate and nitrate + ammonium are
not really independent nutrients in PISCES. They are linked
by a constant and identical Redfield ratio in all the modeled organic compartments, but the nitrogen pool undergoes nitrogen fixation and denitrification in the open ocean
and the upper sediments. Furthermore, their external sources
(rivers, dust deposition) are not linked by a constant ratio.
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O. Aumont et al.: A description of PISCES-v2
sink at the same speed as the large organic matter particles.
An earlier version of PISCES had included a simple description of this ballast effect (Gehlen et al., 2006) but it has been
abandoned since as observations do not suggest a clear relationship between sinking speeds and mineral composition of
particles (Lee et al., 2009). All the non-living compartments
experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM.
In addition to the ecosystem model, PISCES also simulates dissolved inorganic carbon, total alkalinity and dissolved oxygen. The latter tracer is also used to define the regions where oxic or anoxic degradation processes take place.
4
Figure 1. Architecture of PISCES. This figure only shows the
ecosystem model omitting thus oxygen and the carbonate system.
The elements which are explicitly modeled are indicated in the left
corner of each box.
This means that if the latter three processes (nitrogen fixation, denitrification, and external sources) are deactivated
and if the initial distributions of nitrate + ammonium and
phosphate are identical, the simulated fields of both nutrients
should remain identical.
Four living compartments are represented: two phytoplankton size classes/groups corresponding to nanophytoplankton and diatoms, and two zooplankton size classes
which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, iron,
chlorophyll and silicon biomasses (the latter only for diatoms). This means that the Fe / C and Chl / C ratios of both
phytoplankton groups as well as the Si / C ratio of diatoms
are prognostically predicted by the model. For zooplankton, only the total biomass is modeled. For all species, the
C / N / P / O2 ratios are assumed constant and are not allowed to vary. In PISCES, the Redfield ratios C / N / P are
set to 122/16/1 (Takahashi et al., 1985) and the −O / C ratio
is set to 1.34 (Kortzinger et al., 2001). In addition, the Fe / C
ratio of both zooplankton groups is kept constant. No silicified zooplankton is assumed. The bacterial pool is not yet
explicitly modeled.
There are three non-living compartments: semi-labile dissolved organic matter, small sinking particles and large sinking particles. As for the living compartments, the C, N and P
pools are not distinctly modeled. Thus, constant Redfield ratios are imposed for C / N / P. On the other hand, the iron, silicon and calcite pools of the particles are explicitly modeled.
As a consequence, their ratios are allowed to vary. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (“the ballast effect”, Honjo, 1996;
Armstrong et al., 2002). The latter particles are assumed to
Geosci. Model Dev., 8, 2465–2513, 2015
Model equations
The reader should be aware that in the following equations,
the conversion ratios between the different elements (Redfield ratios) have been generally omitted except when particular parameterizations are defined. All phytoplankton and
zooplankton biomasses are in carbon units (mol C L−1 ) except for the silicon, chlorophyll and iron content of phytoplankton, which are respectively in Si, Chl and Fe units
(mol Si L−1 , g Chl L−1 , and mol Fe L−1 , respectively). Finally, all parameters and their standard values in PISCES are
listed in Tables 1a–e at the end of this section.
4.1
Phytoplankton
4.1.1
Nanophytoplankton
P
∂P
= (1 − δ P )µP P − mP
P − sh × wP P 2
∂t
Km + P
− g Z (P )Z − g M (P )M
(1)
In this equation, P is the nanophytoplankton biomass, and
the five terms on the right-hand side represent growth, mortality, aggregation and grazing by micro- and mesozooplankton. The mortality term is modulated by a hyperbolic function of P to avoid extinction of nanophytoplankton at very
low growth rates.
In PISCES, the growth rate of nanophytoplankton (µP )
can be computed according to two different parameterizations:
µP = µP f1 (Lday )f2 (zmxl )
P
−α P θ Chl, PARP
1 − exp
Lday (µref + bresp )
!!
LPlim ,
(2a)
LPlim ,
(2b)
µP = µP f1 (Lday )f2 (zmxl )
P
−α P θ Chl, PARP
1 − exp
Lday µP LPlim
!!
where bresp is a small respiration rate and µref a reference growth rate, independent of temperature. All other
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Table 1. (a) Model parameters for phytoplankton with their default values in PISCES. (b) Model parameters for zooplankton with their
default values in PISCES. (c) Model parameters for DOM with their default values in PISCES. (d) Model parameters for particulate organic
and inorganic matter with their default values in PISCES. (e) Model parameters for various processes with their default values in PISCES.
(a)
Parameter
Units
Value
Description
µ0max
µref
bresp
bP
αI
δI
β1I
β2I
β3I
I,min
KPO
d−1
d−1
d−1
–
(W m−2 )−1 d−1
–
–
–
–
nmol P L−1
0.6
1.0
0.033
1.066
2; 2
0.05; 0.05
2.1; 1.6
0.42; 0.69
0.4; 0.7
0.8; 2.4
Growth rate at 0 ◦ C
Growth rate reference for light limitation
Basal respiration rate
Temperature sensitivity of growth
Initial slope of P –I curve
Exudation of DOC
Absorption in the blue part of light
Absorption in the green part of light
Absorption in the red part of light
Minimum half-saturation constant for phosphate
µmol N L−1
0.013; 0.039
Minimum half-saturation constant for ammonium
µmol N L−1
0.13; 0.39
Minimum half-saturation constant for nitrate
µmol Si L−1
µmol Si L−1
µmol Si L−1
nmol Fe L−1
–
mol Si (mol C)−1
µmol Fe (mol C)−1
1
16.6
2; 20
1; 3
3; 3
0.159
7; 7
Minimum half-saturation constant for silicate
Parameter for the half-saturation constant
Parameters for Si / C
Minimum half-saturation constant for iron uptake
Size ratio of Phytoplankton
Optimal Si / C uptake ratio of diatoms
Optimal iron quota
µmol Fe (mol C)−1
d−1
d−1 mol C−1
d−1 mol C−1
mg Chl (mg C)−1
mg Chl (mg C)−1
µmol C L−1
40; 40
0.01; 0.01
0.01
0.03
0.033; 0.05
0.0033
1; 1
Maximum iron quota
phytoplankton mortality rate
Minimum quadratic mortality of phytoplankton
Maximum quadratic mortality of diatoms
Maximum Chl / C ratios of phytoplankton
Minimum Chl / C ratios of phytoplankton
Threshold concentration for size dependency
4
I,min
KNH
4
I,min
KNO
3
D,min
KSi
KSi
I
KSi
I,min
KFe
I
Srat
Si,D
θm
Fe,I
θopt
Fe,I
θmax
mI
wP
D
wmax
Chl,I
θmax
Chl
θmin
Imax
terms in these equations are defined below. The choice
between the two different formulations is made through
a parameter in the namelist (ln_newprod). When
ln_newprod is set to true, which is the default option of PISCES, Eq. (2a) is used. In the previous equations, Lday is day length (∈ [0, 1]). f1 (Lday ) expresses
the dependency of growth rate to the length of the day
(Gilstad and Sakshaug, 1990; Thompson, 1999). zmxl is the
depth of the mixed layer and f2 (zmxl ) imposes an additional
reduction of the growth rate when the mixed layer depth exceeds the euphotic depth:
f1 (Lday ) = 1.5
Lday
,
0.5 + Lday
(3a)
1z = max (0, zmxl − zeu ) ,
(3b)
tdark = (1z)2 /86 400,
tdark
f2 (zmxl ) = 1 − P
,
tdark + tdark
(3c)
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(3d)
where zeu is the depth of the euphotic zone defined as the
P
depth at which there is 1 ‰ of surface PAR. tdark
is set to
3 days for nanophytoplankton and 4 days for diatoms, as diatoms generally better cope with prolonged dark periods.
tdark is an estimate of the mean residence time of the phytoplankton cells within the unlit part of the mixed layer, assuming a vertical diffusion coefficient of 1 m2 s−1 ; 86 400 converts tdark from s−1 to day−1 . Figure 2 displays f2 (zmxl ) as
a function of 1z.
µP is defined as follows (Eppley, 1972):
fP (T ) = bPT ,
(4a)
µP = µ0max fP (T ).
(4b)
In PISCES, vertical penetration of the photosynthetic
available radiation (PAR) is based on a simplified version of
the model by Morel (1988), which is described in Lengaigne
et al. (2007). Visible light is split into three wavebands: blue
(400–500 nm), green (500–600 nm) and red (600–700 nm).
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Table 1. Continued.
(b)
Parameter
Units
Value
Description
bZ
I
emax
σI
γI
I
gm
M
gFF
I
KG
I
pP
I
pD
I
pPOC
M
pZ
I
Fthresh
Z
Jthres
M
Jthres
mI
rI
Km
νI
θ Fe,Zoo
–
–
–
–
d−1
(m mol L−1 )−1
µmol C L−1
–
–
–
–
µmol C L−1
µmol C L−1
µmol C L−1
(µmol C L−1 )−1 d−1
d−1
µmol C L−1
–
µmol Fe mol C−1
1.079; 1.079
0.3; 0.35
0.3; 0.3
0.6; 0.6
3; 0.75
2 × 103
20; 20
1; 0.3
0.5; 1
0.1,0.3
1.0
0.3; 0.3
0.001
0.001
0.004; 0.03
0.03,0.005
0.2
0.5; 0.75
10
Temperature sensitivity term
Maximum growth efficiency of zooplankton
Non-assimilated fraction
Excretion as DOM
Maximum grazing rate
Flux feeding rate
Half-saturation constant for grazing
Preference for nanophytoplankton
Preference for diatoms
Preference for POC
Preference for microzooplankton
Food threshold for zooplankton
Specific food thresholds for microzooplankton
Specific food thresholds for mesozooplankton
Zooplankton quadratic mortality
Zooplankton linear mortality
Half-saturation constant for mortality
Fraction of calcite that does not dissolve in guts
Fe / C ratio of zooplankton
Table 1. Continued.
(c)
Parameter
Units
Value
Description
λDOC
KDOC
Bact
KNO
3
Bact
KNH
4
Bact
KPO
4
Bact
KFe
a1
a2
a3
a4
a5
d−1
µmol C L−1
µmol N L−1
µmol N L−1
µmol P L−1
nmol Fe L−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
0.3
417
0.03
0.003
0.003
0.01
0.37
102
3530
5095
114
Remineralization rate of DOC
Half-saturation constant for DOC remin.
NO3 half-saturation constant for DOC remin.
NH4 half-saturation constant for DOC remin.
PO4 half-saturation constant for DOC remin.
Fe half-saturation constant for DOC remin.
Aggregation rate (turbulence) of DOC→POC
Aggregation rate (turbulence) of DOC→POC
Aggregation rate (turbulence) of DOC→GOC
Aggregation rate (Brownian) of DOC→POC
Aggregation rate (Brownian) of DOC→POC
For each waveband, the chlorophyll-dependent attenuation
coefficients are fitted to the coefficients computed from the
full spectral model of Morel (1988) (as modified in Morel
and Maritorena, 2001) assuming the same power-law expression. At the sea surface, visible light is split equally between
the three wavebands. PAR can be a constant or a variable
fraction of the downwelling shortwave radiation, as specified
in the namelist (ln_varpar).
ρpar
PAR1 (0) = PAR2 (0) = PAR3 (0) =
SW
3
PARP (z) = β1P PAR1 (z) + β2P PAR2 (z) + β3P PAR3 (z)
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(5a)
(5b)
Light absorption by phytoplankton depends on the waveband and on the species. The normalized coefficients βi have
been computed for each phytoplankton group by averaging
and normalizing, for each waveband, the absorption coefficients published in Bricaud et al. (1995).
In PISCES, the nutrient limitation terms are defined as follows:
LPlim = min LPPO4 , LPN , LPFe ,
(6a)
PO4
,
P
PO4 + KPO
4
(6b)
LPPO4 =
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Table 1. Continued.
(d)
Parameter
Units
Value
Description
λPOC
wPOC
min
wGOC
wdust
a6
a7
a8
a9
λmin
Fe
λFe
λdust
Fe
λCaCO3
nca
0
χlab
slow
λPSi
λfast
PSi
d−1
0.025
2
30
2
25.9
4452
3.3
47.1
3 × 10−5
0.005
150
0.197
1
0.5
0.003
0.025
Degradation rate of POC
Sinking speed of POC
Minimum sinking speed of GOCb
Sinking speed of dust
Aggregation rate (turbulence) of POC→GOC
Aggregation rate (turbulence) of POC→GOC
Aggregation rate (settling) of POC→GOC
Aggregation rate (settling) of POC→GOC
Minimum scavenging rate of iron
Slope of the scavenging rate of iron xlam1
Scavenging rate of iron by dust
Dissolution rate of calcite
Exponent in the dissolution rate of calcite
Proportion of the most labile phase in PSi
Slow dissolution rate of BSi
Fast dissolution rate of BSi
m d−1
m d−1
m s−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
(µmol C L−1 )−1 d−1
d−1
d−1 µmol−1 L
d−1 mg−1 L
d−1
–
–
d−1
d−1
Table 1. Continued.
(e)
Parameter
Units
Value
Description
λNH4
O2 min,1
O2 min,2
LT
m
Nfix
Dz
KFe
Efix
Feice
sed
FFe,min
SolFe
Out
2
Onit
2
?
rNH
4
?
rNO
3
θ N,C
rCaCO3
d−1
µmol O2 L−1
µmol O2 L−1
nmol L−1
µmol N L−1 d−1
nmol Fe L−1
W m−2
nmol Fe L−1
µmol Fe m−2 d−1
–
mol O2 (mol C)−1
mol O2 (mol C)−1
mol N (mol C)−1
mol N (mol C)−1
mol N (mol C)−1
–
0.05
1
6
0.6
0.013
0.1
50
15
2
0.02
133/122
32/122
3/5
105/16
16/122
0.3
Maximum nitrification rate
Half-saturation constant for denitrification
Half-saturation constant for denitrification
Total concentration of iron ligands
Maximum rate of nitrogen fixation
Fe half-saturation constant of nitrogen fixation
Photosynthetic parameter of nitrogen fixation
iron concentration in sea ice
Maximum sediment flux of Fe
Solubility of iron in dust
O / C for ammonium-based processes
O / C ratio of nitrification
C/N ratio of ammonification
C/N ratio of denitrification
N / C Redfield ratio
Rain-ratio parameter
LPN = LPNO3 + LPNH4 ,
P NH
KNO
4
3
LPNH4 = P
,
P + K P NO + K P NH
KNO3 KNH
3
4
NH4
NO3
4
P NO
KNH
3
4
,
LPNO3 = P
P
P
P NH
KNO3 KNH4 + KNH4 NO3 + KNO
4
3
!!
Fe,P
θ Fe,P − θmin
P
LFe = min 1, max 0,
.
Fe,P
θopt
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(6c)
(6d)
(6e)
(6f)
As already stated in the introduction, PISCES is a mixed
Monod–quota model. Thus, N and P limitations are based on
a Monod parameterization where growth depends on the external nutrient concentrations, whereas Fe limitation is modeled according to a classical quota approach. It should be
Fe,P
noted here that for iron, an optimal quota (θopt
) is used in
the denominator which allows luxury uptake as in the model
proposed by Buitenhuis and Geider (2010).
The choice of the half-saturation constants is rather difficult as observations show that they can vary by several orGeosci. Model Dev., 8, 2465–2513, 2015
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O. Aumont et al.: A description of PISCES-v2
relationship, which remains within the estimated range and
which can also be derived from simple volumetric considerations (surface-to-volume ratio). The three parameters in
P ) can be independently
this equation (Pmax , KiP ,min , and Srat
specified for each phytoplankton group. Finally, observations
also suggest that these half-saturation constants should vary
with the mean nutrient concentrations, probably as an acclimation to the local environment (Collos et al., 1980; Smith
et al., 2009). This acclimation mechanism is not included in
PISCES, except for the case of silicate (see Sect. 4.1.2).
The distinction between new production based on nitrate
and regenerated production based on ammonium is computed as follows (O’Neill et al., 1989):
µPNO3 = µP
Figure 2. Reduction of growth rate when the mixed layer depth
exceeds the euphotic depth for nanophytoplankton (continuous line)
and diatoms (dashed line). Depth corresponds to 1Z.
LPNO3
LPNO3 + LPNH4
µPNH4 = µP
LPNH4
LPNO3 + LPNH4
, (8)
where µPNO3 and µPNH4 are the uptake rates of nitrate and ammonium, respectively.
The nanophytoplankton aggregation term wP depends on
the shear rate (sh), as the main driver of aggregation is the
local turbulence. This shear rate is set to 1 s−1 in the mixed
layer and to 0.01 s−1 below. This means that the aggregation
is reduced by a factor of 100 below the mixed layer.
ders of magnitude (e.g., Perry, 1976; Sommer, 1986; Donald
et al., 1997). However, in general, these constants increase
with the size of the phytoplankton cell as a consequence
of a smaller surface-to-volume ratio (diffusive hypothesis)
(Eppley et al., 1969). Thus, diatoms will tend to have larger
half-saturation constants than nanophytoplankton. However,
in PISCES, phytoplankton are modeled by only two compartments, each of them encompassing a large range. Experiments performed with the model have shown that results are
sensitive to the choice of these half-saturation constants.
Following these remarks, it appeared not appropriate to
keep the nutrient half-saturation constants constant. It was
then decided to make them vary with the phytoplankton
biomass of each compartment because the observations show
that the increase in biomass is generally due to the addition
of larger size classes of phytoplankton (e.g., Raimbault et al.,
1988; Armstrong, 1994; Hurtt and Armstrong, 1996):
In this equation, D is the nanophytoplankton biomass, and
the five terms on the right-hand side represent growth, mortality, aggregation and grazing by micro- and mesozooplankton.
As for nanophytoplankton, the absorption coefficients of
diatoms depend on the considered waveband:
P1 = min (P , Pmax ) ,
(7a)
PARD = β1D PAR1 + β2D PAR2 + β3D PAR3 .
P2 = max (0, P − Pmax ) ,
(7b)
P P
P1 + Srat
2
,
KiP = KiP ,min
P1 + P2
(7c)
P is the size ratio of the larger size class over the
where Srat
smaller size class. KiP ,min is the half-saturation constant of
the smaller size class. This parameterization assumes that
half-saturation constants increase linearly with size (Eppley
et al., 1969). The size dependence of these constants with
cell size is not necessarily linear but has been suggested to
follow a power-law function with an exponent lower than
1 (Litchman et al., 2007). However, in a recent review, Edwards et al. (2012) found an exponent close to 1 for nitrogen
(linear relationship) and larger than 1 for phosphorus. Thus,
considering these uncertainties, we decided to keep a linear
Geosci. Model Dev., 8, 2465–2513, 2015
4.1.2
Diatoms
∂D
D
=(1 − δ D )µD D − mD
D − sh × wD D 2
∂t
Km + D
− g Z (D)Z − g M (D)M
(9)
(10)
The production terms for diatoms are defined as for
nanophytoplankton, except that the limitation terms also include Si:
D
D
D
D
LD
=
min
L
,
L
,
L
,
L
(11a)
N
Fe
lim
PO4
Si ,
LD
Si =
Si
.
D
Si + KSi
(11b)
As for the other nutrients, the half-saturation factor of silicate can vary significantly over the ocean. In the tropical
and temperate regions, this factor is around 1 µM, whereas
values as high as 88.7 µM have been measured for Antarctic species (Sommer, 1986; Martin-Jézéquel et al., 2000). In
that case, rather than an effect of the cell size, these variations are a consequence of an acclimation of the cells to
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O. Aumont et al.: A description of PISCES-v2
2473
their local environment. When plotted against maximum local yearly concentration of silicate, a crude relationship can
be inferred (Pondaven et al., 1998):
D,min
D
KSi
= KSi
+
7 S̆i2
(KSi )2 + S̆i2
(12)
,
where S̆i here is the maximum Si concentration over a year
(note that during the first year of a pluriannual simulation, S̆i
is set to a constant). For the other nutrients, we use the same
parameterization as for nanophytoplankton (see Eq. 7).
The diatoms aggregation term wpD is increased in case of
nutrient limitation because it has been shown that diatoms
cells tend to excrete a mucus (exocellular polysaccharides,
EPS) which increases their stickiness. As a consequence, collisions between cells yield to a more efficient aggregation
process (Smetacek, 1985; Decho, 1990):
4.1.4
The temporal evolution of the iron biomass of phytoplankton
I Fe (model units are mol Fe L−1 ), where I denotes P or D,
is driven by the following equation
I
∂I Fe
Fe
= (1 − δ I )µI I − mI
I Fe − sh × w I I I Fe
∂t
Km + I
− θ Fe,I g Z (I )Z − θ Fe,I g M (I )M.
(16)
Iron in phytoplankton is modeled in PISCES according to
a classical quota approach. However, to be consistent with
chlorophyll and silica, we model the iron biomass of phytoplankton (I Fe ) rather than the iron quota (θ Fe,I ) directly.
Growth rate of the iron biomass of phytoplankton is parameterized according to
Fe,I
I Fe
µ
D
w =w
P
D
+ wmax
(1 − LD
lim ).
Chlorophyll in nanophytoplankton and diatoms
Chlorophyll biomass
(where I denotes P or D, typical
units are µg Chl L−1 or mg Chl m−3 ) for both phytoplankton
groups is parameterized using the photo-adaptive model of
Geider et al. (1997):
∂I Chl
I
Chl + (θ Chl,I − θ Chl )ρ I Chl )µI I − mI
I Chl
= (1 − δ I )(12θmin
max
min
Km + I
∂t
−sh × wI I I Chl − θ Chl,I g Z (I )Z − θ Chl,I g M (I )M,
(14)
where I is the phytoplankton group and θ Chl,I is the
chlorophyll-to-carbon ratio of the considered phytoplankton
Chl
class; 12 represents the molar mass of carbon; ρ I the ratio of energy assimilated to energy absorbed as defined by
Geider et al. (1996):
Chl
=
144µ̆I I
I
α I I Chl PAR
Lday
(15a)
,
−α I θ Chl,I PARI
µ̆ = µP f2 (zmxl ) 1 − exp
Lday µP LIlim
I
LIlim .
(15b)
1 − θ Fe,I
θmax
Fe,I
1.05 − θ Fe,I
µP .
(17)
θmax
As in Flynn and Hipkin (1999), iron uptake is also downregulated via a feedback from θ Fe,I using a normalized inverse hyperbolic function with a small shape factor set to
0.05.
Fe
In the former equation, LIlim,1 is the iron limitation term
and is modeled as follows:
bFe
Fe
LIlim,1 =
Fe
I
bFe + KFe
,
I I
I1 + Srat
2
,
I1 + I2
I2 = max (0, I − Imax ) , I1 = I − I2 ,
Fe
Fe,min
I
I
KFe
= KFe
(18a)
(18b)
(18c)
where bFe is the concentration of bioavailable iron (see
Sect. 4.5.3). The half-saturation constant for iron uptake is
also increasing with phytoplankton biomass as for the other
half-saturation constants (see Eq. 7).
At low iron concentrations, observations suggest that iron
uptake might be enhanced, at least for some species (Harrison and Morel, 1986; Doucette and Harrison, 1991), giving
surge uptake. Morel (1987) proposed a parameterization of
both this surge uptake and the downregulation of iron uptake
at high iron quota (see above) which has been included in the
recent model of Buitenhuis and Geider (2010). In PISCES,
a different parameterization has been chosen since downregulation is already included in Eq. (17):
!!
In this equation, 144 is the square of the molar mass of
C and is used to convert from mol to mg, as the standard
unit for Chl is generally in mg Chl m−3 . It should be noted
that for chlorophyll synthesis, the second parameterization
of phytoplankton growth is used to compute µ̆I (see Eq. 2b).
I .
This is necessary because of the expression for ρChl
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I Fe
Fe,I
= θmax
Llim,1 Llim,2
I Chl
ρI
I Fe
(13)
Furthermore, as for nanophytoplankton, the aggregation
is multiplied by the shear rate. Enhanced aggregation rates
when diatoms are stressed result in a rapid decline of the diatoms blooms when nutrients become exhausted and produce
strong export events.
4.1.3
Iron in nanophytoplankton and diatoms
Fe
LIlim,2 =
4 − 4.5LIFe
LIFe + 0.5
.
(19)
Llim,2 equals 4 at very low iron concentrations and 1
at high iron concentration. Overall, the downregulation in
Eq. (17) together with the surge uptake induced by the previous equation results in a behavior of the system that is qualitatively equivalent to what results from the parameterization
of Buitenhuis and Geider (2010).
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The demands for iron in phytoplankton are for photosynthesis, respiration and nitrate/nitrite reduction. Following
Flynn and Hipkin (1999), we assume that the rate of synthesis by the cell of new components requiring iron is given by
the difference between the iron quota and the sum of the iron
required by these three sources of demand, which we defined
as the actual minimum iron quota:
0.0016 Chl,I 1.21 × 10−5 × 14 P
θ
+
L
55.85
55.85 × 7.625 N
1.15 × 10−4 × 14 P
× 1.5 +
L .
(20)
55.85 × 7.625 NO3
In this equation, the first right term corresponds to photosynthesis, the second term corresponds to respiration and
the third term estimates nitrate and nitrite reduction. The parameters used in this equation are directly taken from Flynn
and Hipkin (1999). The modeled iron quota in PISCES varies
Fe,I
thus between this minimum quota θmin
and the maximum
Fe,I
quota θmax , i.e., between about 1 and 40 µmol Fe (mol C)−1
when using the standard set of parameters (see Table 1).
Fe,I
θmin
=
4.1.5
Silicon in diatoms
Si
D Si
Flim,2
= min 1, 2.2max 0, LD
,
lim,1 − 0.5
Si
LD
lim,1 =
Si
LD
lim,2 =
4.2.1
(21)
The elemental ratio Si / C (or Si / N) has been observed to
vary by a factor of about 4 to 5 over the global ocean with
a mean value around 0.14 ± 0.13 mol mol−1 (Sarthou et al.,
2005). Light, N, P, or Fe stress has been demonstrated to lead
to heavier silicification (e.g., Takeda, 1998; Franck et al.,
2000; Martin-Jézéquel et al., 2000). It has been suggested
that these elevated elemental ratios result from the physiological adaptation of the silicon uptake by the cell depending
on the growth rate and on the G2 cycle phase during which Si
is incorporated (Martin-Jézéquel et al., 2000; Claquin et al.,
2002). Lighter silicification can only result from silicate limitation.
We model the variations of the Si / C ratio following the
parameterization proposed by Bucciarelli et al. (2002, unpublished manuscript):
Si
Si,D
θopt
= θmSi,D LD
lim,1
Si
D Si
D Si
min 5.4, 4.4 exp −4.23Flim,1
Flim,2
+ 1 1 + 2LD
.
lim,2
(22)
Relative to the original parameterization, an additional
D Si ) to produce
limitation term by Si has been added (Flim,2
a lighter silicification in case of Si exhaustion.
The different terms in Eq. (22) are defined as follows:
!
µD
D
D
D
D Si
, LPO4 , LN , LFe ,
(23a)
Flim,1 = min
µP LD
lim
Geosci. Model Dev., 8, 2465–2513, 2015
2 )3
Si3 +(KSi
0
(23c)
if ϕ < 0
(23d)
if ϕ > 0,
where ϕ is the latitude. In the Southern Ocean, observations
show that diatoms are very heavily silicified. After correcting for the potential effects of iron limitation, silicification
in the Southern Ocean is at least 3 times stronger than in
the tropical regions, which can only be explained by the diatoms morphological types (Baines et al., 2010). To reproduce those high Si / C ratios, we have introduced the term
Si
LD
lim,2 which increases the Si / C ratio by a factor of up to 3
when silicate concentrations are high, a specific characteristics of the Southern Ocean. This increase is restricted to the
2.
Southern Hemisphere and is controlled by the parameter KSi
This parameter is set in the namelist and thus, if it is set to
a very high value, then no increase of Si / C at high silicate
concentrations is predicted by the model.
4.2
∂D Si
Si,D
(1 − δ D )µD D − θ Si,D g M (D)M
= θopt
∂t
D
− θ Si,D g Z (D)Z − mD
D Si
Km + D
− sh × wD DD Si
Si
,
1
Si + KSi
( Si3
(23b)
Zooplankton
Microzooplankton
∂Z
= eZ g Z (P ) + g Z (D) + g Z (POC) Z
∂t
− g M (Z)M − mZ fZ (T )Z 2
Z
Z
− r fZ (T )
+ 31(O2 ) Z
Km + Z
(24)
In this equation, Z is the microzooplankton biomass, and
the four terms on the right-hand side represent growth, grazing by mesozooplankton, quadratic and linear mortalities.
The grazing rate depends on temperature according to
a typical exponential relationship similar to what is used for
phytoplankton:
Z
0,Z
gm
= gmax
fZ (T ),
(25a)
T
fZ (T ) = bZ
,
(25b)
0,Z
where gmax
is the maximum grazing rate at 0 ◦ C, bZ is the
temperature dependence and T is the temperature. In their re10 )
view, Buitenhuis et al. (2010) have found a Q10 (Q10 = bZ
between 1.7 and 2.2. Lower temperature dependences were
found in laboratory experiments compared to what as been
identified in the field. In PISCES, we have set Q10 to 2.14
which is not only close to the value found in the field but
also close to the value chosen for mesozooplankton (see below). All terms driving the temporal evolution of microzooplankton have been assigned the same temperature dependence. Mortality is enhanced when oxygen is depleted. In
other words, microzooplankton (but also mesozooplankton,
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2475
see below) are treated as being unable to cope with anoxic
waters. This increased mortality also avoids respiration in
waters devoid of oxygen.
Grazing on each species I is defined as
X
Z
F=
pJZ max 0, J − Jthresh
J
Z
Flim = max 0, F − min 0.5F, Fthresh
Z
Z
Z
Z Flim pI max 0, I − Ithresh
,
g (I ) = gm
P
F
KGZ + J pJZ J
(26a)
where J denotes all the species microzooplankton can graze
upon (P , D and POC) and pJZ is the preference microzooplankton has for each J . In PISCES, we have chosen
a Michaelis–Menten parameterization with no switching and
Z
a threshold (Fthresh
) (Gentleman et al., 2003). This choice is
rather arbitrary. Another very popular formulation in models is the Michaelis–Menten parameterization with active
switching introduced by Fasham et al. (1990). However, this
parameterization exhibits anomalous dynamics such as suboptimal feeding (Gentleman et al., 2003). In our parameZ
terization, a threshold for each individual resource (Jthresh
)
Z
can be specified in addition to the global threshold (Fthresh
).
For low food abundance, this global threshold is allowed to
slowly decrease to 0 as a function of the total food level to
maintain some grazing pressure, in particular in the ocean
interior.
Responses of zooplankton to quality of their preys have
been termed stoichiometric modulation of predation (SMP)
by Mitra and Flynn (2005). A complete review of the different expected responses has been presented by Mitra et al.
(2007). For instance, when confronted with poor food quality, zooplankton can increase their ingestion rate (Plath and
Boersma, 2001; Darchambeau and Thys, 2005), or decrease
it as the food can become deleterious (Flynn and Davidson, 1993). Accounting for the complexities of these different types of behavior has not been implemented within
PISCES as this would require a model with flexible stoichiometry. Additionally, it would require a correct parameterization of the different potential responses and the apparently contradictory nature of observed responses implies that
this task will be very complicated. In PISCES, food quality
is assumed to only affect gross growth efficiency (eZ ): When
food quality becomes poor (either the Fe / C ratio θ Fe,I or
the N / C ratio θ N,I of the preys decreases), eZ decreases:
P Fe,I Z
P N,I Z
Z
I θP g (I )
I θ P g (I )
,
,
(27a)
= min 1, N,C
eN
Fe,Z
Z
Z
θ
I g (I )
I g (I ) θ
P Fe,I Z
Z
Z
Z
Z
I θ P g (I )
.
(27b)
e = eN min emax , (1 − σ ) Fe,Z
Z
θ
I g (I )
When the Fe / C ratio of the ingested preys becomes lower
than the zooplankton Fe / C ratio, the excess carbon (and nutrients) is lost as dissolved inorganic and organic carbon (and
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nutrients). This is described in PISCES by a decrease in the
carbon gross growth efficiency (Eq. 27b). By construction in
PISCES, the N / C quota is constant, so this quota is estimated by solving the classical Droop equation assuming that
it is at steady state (see above the definition of θ N,I ).
4.2.2
Mesozooplankton
∂M
M
= eM g M (P ) + g M (D) + g M (POC) + gFF
(GOC)
∂t
M
+gFF
(POC) + g M (Z) M
− mM fM (T )M 2 − r M fM (T )
M
+ 31(O2 ) M
Km + M
(28)
In this equation, M is the mesozooplankton biomass, and
the three terms on the right-hand side represent growth,
quadratic and linear mortalities. All terms in this equation
have been assigned the same temperature dependence using
a Q10 of 2.14 (Buitenhuis et al., 2005).
Parameterization of mesozooplankton grazing is similar to microzooplankton. In addition to the “conventional”
concentration-dependent grazing described by Eq. (26a), flux
feeding is also accounted for in PISCES. This type of grazing has been shown to be potentially very important for the
fate of particles in the water column below the euphotic zone
(Dilling and Alldredge, 2000; Stemmann et al., 2004). Flux
feeding depends on the flux and thus, on the product of the
concentration by the sinking speed. In PISCES, both the
small and the large particles experience this type of grazing:
M
gFF
(POC) = gFF fM (T )wPOC POC,
(29a)
M
gFF
(GOC) = gFF fM (T )wGOC GOC.
(29b)
This importance of flux feeding has been analyzed in
PISCES by Gehlen et al. (2006). They have shown that flux
feeding is the most important process that controls the flux
of particulate organic carbon below the surface mixed layer.
In Eq. (28), the term with a quadratic dependency to
mesozooplankton does not depict aggregation but grazing by
the higher, non-resolved trophic levels. Following Anderson
et al. (2013), the upper trophic levels are modeled assuming an infinite chain of carnivores. This assumption permits
one to easily compute the production of fecal pellets as well
as the respiration and excretion by these non-resolved carnivores:
M
M
Pup
= σ M fup (emax
)mM fM (T )M 2 ,
M
Rup
= (1 − σ
M
M
M
− emax
)fup (emax
)mM fM (T )M 2 ,
(30a)
(30b)
where function fup (x) is
fup (x) =
∞
X
i=0
xi =
1
1−x
for
0 < x < 1.
(31)
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It should be noted here that a similar quadratic term is also
included in the equation for microzooplankton (see Eq. 26a)
despite the fact that their predators are (at least partially) represented in PISCES. In that case, this term rather represents
other density-dependent mortality factors such as viral diseases. As a consequence, the assumption of an infinite chain
of carnivores is not used for microzooplankton and everything is routed to POC.
4.3
DOC
The temporal evolution of DOC is driven by the following
equation
X
∂DOC
= (1 − γ Z )(1 − eZ − σ Z ) g Z (I )Z
∂t
I
M
M
,
− 8DOC
− 8DOC
− 8DOC
3
2
1
O2
Bact
, λDOC fP (T ) (1 − 1(O2 )) Lbact
DOC ,
lim
ut
Bactref
O2
(33a)
!
Denit = min
(34e)
bact
bact
Lbact
N = LNO3 + LNH4 ,
(34f)
NO3
Bact
, λDOC fP (T )1(O2 )Lbact
DOC .
lim
?
rNO
Bact
ref
3
(33b)
Remineralization of DOC can be either oxic (Remin) or
anoxic (Denit) depending on the local oxygen concentration. The distinction between the two types of organic matter
degradation is performed using a factor 1(O2 ) that varies
between 0 and 1 (see Sect. 4.5.1 for the formulation of this
factor). It is assumed that the specific rates of degradation
(λDOC ) specified for respiration and denitrification are identical.
Geosci. Model Dev., 8, 2465–2513, 2015
bact
bFe + KFe
PO4
bact
PO4 + KPO
4
bact K bact
KNO
3 NH4
(32)
where I includes P , D and POC for microzooplankton and
P , D, Z and POC for mesozooplankton (see Eqs. 24 and 28,
respectively). In the following, DOM and DOC will be used
indifferently since the stoichiometric ratios in dissolved organic matter are assumed constant in PISCES.
Marine DOM has traditionally been divided into several
fractions characterized by their lability. DOM, which recycles over timescales of a few months to a few years, is called
semi-labile DOM (Anderson and Williams, 1999). Transport
of this pool of dissolved organic matter can make a significant part of the carbon pump (Carlson et al., 1994; Anderson
and Williams, 1999). As a consequence, this important pool
of DOM is modeled in PISCES. The labile and refractory
pools of DOM are not explicitly modeled.
The degradation of semi-labile DOC is parameterized as
follows:
(34c)
,
Lbact
NH4 =
M
+ (1 − γ M )Rup
− Remin − Denit
(34b)
(34d)
Lbact
PO4 =
+ δ µP P + λ?POC POC
bFe
(34a)
,
M
I
P
bact
Lbact = Lbact
lim LDOC ,
DOC
,
Lbact
DOC =
DOC + KDOC
bact
bact
bact
,
L
Lbact
=
min
L
,
L
,
NH
Fe
PO4
lim
4
Lbact
Fe =
+ (1 − γ )(1 − e − σ )
!
X
Z
M
g (I ) + gFF (GOC) M + δ D µD D
Remin = min
Depending on the quality of the organic matter, bacteria may take up nutrients from seawater
(e.g., Goldman and Dennett, 1991; Thingstad and Lignell, 1997),
and thus may be limited by their availability. Of course,
bacterial production is also limited by the abundance of
dissolved organic matter. Therefore, we parameterize the
regulation of the degradation of DOM by bacterial activity
(Lbact ) according to
Lbact
NO3 =
bact K bact
KNO
3 NH4
bact NH
KNO
4
3
,
bact
bact NH
+ KNH4 NO3 + KNO
4
3
bact NO
KNH
3
4
.
bact NO + K bact NH
+ KNH
4
3
NO
4
3
(34g)
(34h)
The half-saturation constants of the P and N limitation
terms (Kibact ) are set in the namelist.
In PISCES, bacterial biomass is not explicitly modeled;
Instead, we use the following formulation:
zmax = max (zmxl , zeu ) ,
(35a)

min (0.7(Z + 2M) , 4 µmol C L−1 ) if z ≤ zmax
0.683
Bact =
Bact(zmax ) zmax
Otherwise.
z
(35b)
In the previous equation, 0.7(Z + 2M) is a proxy for
the bacterial concentration. This relationship has been constructed from an unpublished version of PISCES (already
mentioned in Aumont and Bopp, 2006) that includes an explicit description of the bacterial biomass. Below a certain
depth (zmax ), this biomass decreases with depth via a powerlaw function (Aristegui et al., 2009).
In Eq. (32), the terms 8DOC denote aggregation processes
and are described hereafter (see Sect. 4.4.1). For DOM, we
consider turbulence-induced as well as Brownian aggregation processes.
8DOC
= sh × (a1 DOC + a2 POC)DOC
1
(36a)
8DOC
2
8DOC
3
= sh × a3 GOC × DOC
(36b)
= (a4 POC + a5 DOC)DOC
(36c)
4.4
Particulate organic matter
PISCES includes two different schemes for particulate organic matter:
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2477
– A simple model based on two different size classes
for particulate organic matter. In that case, particulate
organic matter is modeled in PISCES using two tracers corresponding to the two size classes: POC for the
smaller class (1–100 µm) and GOC for the larger class
(100–5000 µm).
– A more complex model proposed by Kriest and Evans
(1999) in which the size spectrum of the particulate organic matter can be represented by a power-law function. Here, particulate organic matter is represented by
two variables: the first (POC) is the carbon concentration and the second (NUM) is the total number of aggregates by unit volume of water.
By default, the simplest parameterization is used. The Kriest model is activated by a cpp key key_kriest.
4.4.1
Two-compartment model of Particulate Organic
Matter (POM)
∂POC
,
∂z
(37)
where wPOC is the vertical sinking speed. For POC, it is set
to a constant value, in general to a small value on the order of
a few meters per day. The fate of mortality and aggregation of
nanophytoplankton depends on the proportion of the calcifying organisms (RCaCO3 ). We assume that 50 % of the organic
matter of the calcifiers is associated with the shell. Since calcite is significantly denser than organic matter, 50 % of the
biomass of the dying calcifiers is routed to the fast sinking
particles. The same is assumed for the mortality of diatoms
as a consequence of the denser density of biogenic silica.
The specific degradation rate λ?POC depends on temperature with a Q10 of about 1.9, the same as for phytoplankton. Furthermore, observations generally tend to show slower
degradation rates when waters are anoxic (Harvey et al.,
1995; Mooy et al., 2002). In Mooy et al. (2002), the attenuation coefficient (b) for the flux was found to be about 0.4
instead of the standard value 0.86 (Martin et al., 1987). This
corresponds to a 45 % decrease of the degradation rate in
anoxic waters relative to oxic waters, which is implemented
as
λ?POC = λPOC fP (T ) (1 − 0.451(O2 )) .
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8 = sh × a6 POC2 + sh × a7 POC × GOC + a8 POC
× GOC + a9 POC2 .
(39)
In this equation, the first two terms correspond to turbulent aggregation, and the two last terms to differential settling
aggregation. The values of the parameters controlling these
processes have been computed offline assuming a steadystate power-law size spectrum for particles with an exponent
of 3.6. Subsequently, the different coagulation kernels (e.g.,
Jackson, 1990; Kriest and Evans, 1999) have been integrated
over the size ranges corresponding to the different compartments. A constant stickiness of 0.1 has been chosen.
The temporal evolution of GOC is written
!
X
∂GOC
M
M
M
M
g (I ) + gFF (POC) + gFF (GOC)
=σ
∂t
I
M
M
M + r M fM (T )
M + Pup
M + Km
P
+ 0.5RCaCO3 mP
P + wP P 2
P + Km
D
+ 0.5mD
Dw D D 2
D + Km
M
− gFF
(GOC)M − λ?POC GOC
+ 8 + 8DOC
2
∂GOC
− wGOC
.
∂z
The temporal evolution of POC is written:
X
D
∂POC
=σZ
g Z (X)Z + 0.5mD
D
∂t
D + Km
Z
+ r Z fZ (T )
Z + mZ fZ (T )Z 2
Z + Km
P
+ (1 − 0.5RCaCO3 )(mP
P + wP P 2 )
P + Km
+ 8DOC
+ λ?POC GOC + 8DOC
3
1
M
M
− g (POC) + gFF (POC) M − g Z (POC)Z
− λ?POC POC − 8 − wPOC
POC experiences aggregation due to turbulence and differential settling:
(38)
(40)
The equation controlling the temporal evolution of GOC
is similar to that of POC. However, some observations have
shown that the mean sinking speed of particulate organic
matter increases with depth (e.g., Berelson, 2002). Such an
increase is consistent with the power-law formulation proposed by Martin et al. (1987). Such an increase in the settling
speed is parameterized in PISCES for GOC as follows:
zmax = max (zeu , zmxl ) ,
min
min
wGOC = wGOC
+ (200 − wGOC
)
(41a)
max (0, z − zmax )
.
5000
(41b)
The parameters in this equation have been adjusted using a model of aggregation/disaggregation with multiple size
classes (Gehlen et al., 2006). The maximum sinking speed is
set to 200 m d−1 and is reached at about 5000 m depth over
most of the ocean since zmax is generally less than 100 m.
We have not included any ballasting effect due to the higher
density of biogenic silica or calcite (Klaas and Archer, 2002;
Armstrong et al., 2002). In fact, observations are rather contradictory on this ballast effect (Lee et al., 2009). In particular, the greater efficiency of the vertical sedimentation of
organic matter when associated with calcite and biogenic silica may be due rather to the protection of an organic matter
fraction by the inorganic matrix (Moriceau et al., 2009; Engel
et al., 2009).
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4.4.2
O. Aumont et al.: A description of PISCES-v2
+ mP
Kriest model of particulate organic matter
D
D + wD D 2
D + Km
Z
+ r Z fZ (T )
Z + mZ fZ (T )Z 2
Z + Km
M
M
+ r M fM (T )
M + Pup
− g M (POC)M
M + Km
− g Z (POC)Z − λ?POC POC
DOC
M
M
+ 8DOC
+
8
−
g
(POC)
+
g
(POC)
M
FF
1
3
Here we present a brief overview of the model of Kriest and
Evans (1999). The reader is referred to the literature, where
the method has been presented (e.g., Kriest and Evans, 1999,
2000; Kriest, 2002), for more detail. The model postulates
that the carbon content (m(di )), the sinking speed (w(di ))
and the abundance of the aggregates (n(di )) can be described
by power-law functions of their diameters (di ):
ζ
m(di ) = Cdi ,
(42a)
w(di ) = Bdiν ,
n(di ) = Adi .
(42b)
=
(ζ + 1)POC − ml NUM
,
POC − ml NUM
(43)
where ml is the mass of the smallest aggregate (of size l).
Having , the average sinking speed of numbers (wNUM )
and mass (wPOC ) can be computed following Kriest (2002):
wPOC = wl
ζ + 1 − + ( Ll )1+ν+ζ − ν
,
1+ν +ζ −
(44a)
1 − + ( Ll )1+ν− ν
.
1+ν −
(44b)
wNUM = wl
The number of particles and the mass of particles change
independently. For instance, sinking tends to remove larger
particles. As a consequence, the relationship between the
number of particles and their mass evolves with time and
space and so does . As a result, the sinking speeds for both
mass and number vary with space and time.
Aggregation (ξ ) depends on the particle abundance, their
size distribution, rate of turbulent shear and the difference in
particle sinking speeds as well as the stickiness (the probability that two particles stick together after contact). The
approach implemented in PISCES follows that described in
Kriest (2002); see Kriest (2002) for the term ξ and its computation. Currently it is assumed that turbulent shear rate is high
in the mixed layer (1 m s−1 ), and low below (0.01 m s−1 ).
Summing up the number of collisions due to turbulent shear
and differential settlement, Csh and Cds , respectively, the decrease of the number of particles due to aggregation is then:
ξ = Stick × (Csh + Cds ).
(45)
In PISCES, the stickiness (the efficiency of the collisions)
is set to a constant value in the namelist.
The temporal evolution of the mass of particles is given as
!
X
X
∂POC
Z
Z
M
M
M
=σ
g (X)Z + σ
g (I ) + gFF (POC) M
∂t
I
Geosci. Model Dev., 8, 2465–2513, 2015
+ w P P 2 + mD
− g Z (POC)Z
(42c)
It is also assumed, as in Kriest (2002), that aggregates
above a certain size L have a constant sinking speed wL .
The slope of the size spectrum can be computed from the
total number of aggregates (NUM) and the total mass of particles (POC), which are the two state variables of the model:
P
P
P + Km
− λ?POC POC − wPOC
∂POC
.
∂z
(46)
This is exactly equal to the sum of the two equations used
for the temporal evolution of POC and GOC in the twocompartment model of PISCES (see Eqs. 37 and 40).
P M
P
M
∂NUM σ Z g Z (X)Z σ M
I g (I ) + gFF (POC) M
=
+
∂t
m̄Z
m̄M
P
P
2
P
m P +Km P + w P
+
m̄P
D
D
m D+Km D + wD D 2
+
m̄D
Z
Z + mZ fZ (T )Z 2
r Z fZ (T ) Z+K
m
+
m̄Z
M
M
M
r fM (T ) M+Km M + Pup
+
m̄M
M (POC) M
g M (POC) + gFF
−
m̄M
Z
8DOC + 8DOC
g (POC)Z
3
− λ?POC POC + 1
−
m̄Z
ml
∂NUM
(47)
− ξ − wNUM
∂z
In this equation, each process affecting the mass of the
particles is divided by the mean mass (m̄) of the compartment
exerting this process to convert to numbers.
4.4.3
Iron in particles
In this subsection, the description corresponds to the twocompartment version of the model. To obtain the Kriest version, the equations for both SFe and BFe, the iron content
of the small and big particles, respectively, should be simply
summed.
X
∂SFe
Z
= σ Z θ Fe,I g Z (I )Z + θ Fe,Z (r Z fZ (T )
Z
∂t
Z
+
Km
I
+ mZ fZ (T )Z 2 )
+ λ?GOC BFe + θ Fe,P (1 − 0.5RCaCO3 )
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O. Aumont et al.: A description of PISCES-v2
2479
P
P + sh × w P P 2 )
P + Km
D
D + λFe POC Fe0
+ θ Fe,D 0.5mD
D + Km
+ Cgfe1 − λ?POC SFe − θ Fe,POC 8
M
− θ Fe,POC g M (POC) + gFF
(POC) M+
and GOC (λFe GOC Fe0 ) is then allocated to SFe and BFe,
respectively.
(mP
SFe
κBact
Bactfe − θ Fe,POC g Z (POC)
∂SFe
− wPOC
,
∂z
X
∂BFe
=σM
θ Fe,I g M (I )
∂t
I
4.4.4
∂PSi
= θ Si,D g M (D)M
∂t
+ θ Si,D g Z (D)Z + θ Si,D mD
− λ?PSi DissSi PSi − wGOC
M
M
M + Pup
)+
M + Km
P
P
θ Fe,P 0.5RCaCO3 (mP
P + Km
+ sh × wP P 2 )
D
D
+ θ Fe,D (0.5mD
D + Km
BFe
+ sh × wD D 2 ) + κBact
Bactfe
+ λFe GOC Fe + θ
M
− θ Fe,GOC gFF
(GOC)M
− wGOC
− λ?POC BFe
(49)
where Fe0 is the free form of dissolved iron. Its determination
is detailed in Sect. 4.5.3. Bactfe is the amount of iron taken
up by bacteria which is lost as particulate organic iron. Its
computation is detailed in Sect. 4.5.3.
The free form of dissolved iron Fe0 is the only form of iron
that is assumed to be susceptible to scavenging. The scavenging rate of iron is made dependent upon the particulate
load of the seawater as follows (e.g., Honeyman et al., 1988;
Parekh et al., 2004):
λ?Fe = λmin
Fe + λFe (POC + GOC + CaCO3 + BSi)
+ λdust
Fe Dust,
(50a)
Scav = λ?Fe Fe0 .
(50b)
Implicitly, in this equation, it is assumed that the affinity of iron for the different types of biogenic particles is the
same. Iron is also scavenged by lithogenic particles originating from dust deposition as evidenced by mesocosm experiments (Wagener et al., 2010). The concentration of lithogenic
particles is estimated as described in Eq. (84). Model estimates (Ye et al., 2011) suggest a different affinity for these
particles compared to biogenic particles, which justifies the
split between biogenic and lithogenic materials in Eq. (50).
The amount of iron that is scavenged by POC (λFe POC Fe0 )
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(51)
968
Sieq = 106.44− T +273.15
Sieq − Si
Sisat =
Sieq
T
?
λPSi = λPSi 0.225 1 +
Sisat
15
!9
T 4
Sisat .
+ 0.775 1 +
400
8 + Cgfe2
∂BFe
,
∂z
∂CaCO3
∂z
The dissolution rate of PSi depends on in situ temperature
and on silicic acid saturation following the parameterization
proposed by Ridgwell et al. (2002):
+ θ Fe,M (r M fM (T )
Fe,POC
D
D Si
Km + D
+ sh × wD DD Si
(48)
M
M
+θ Fe,POC gFF
(POC) + θ Fe,GOC gFF
(GOC) M
0
PSi
(52)
The evolution of λ?PSi as a function of Si and of temperature is shown on Fig. 4.
Laboratory experiments show that the diatom frustule is
made of two biogenic silica phases which dissolve simultaneously, but at different rates (e.g., Kamatani et al., 1980;
Van Capellen et al., 2002; Moriceau et al., 2009; Loucaides
et al., 2012). The first phase dissolves significantly faster than
the second phase. It is associated with membrane lipids and
amino acids and represents about one-third of the frustule
(Moriceau et al., 2009). However, the existence of these two
phases is still a matter of debate as it has been hypothesized
to be a result of the experimental design of the dissolution experiments (Loucaides et al., 2012). In PISCES, despite this
uncertainty, we model silica dissolution using two phases.
The proportion of the most “labile” phase is set to a constant
(χlab ) in the upper ocean and is computed in the rest of the
ocean assuming steady state:
zmax = max (zeu , zmxl )
χlab =
( 0
χlab
0 exp
χlab
if z ≤ zmax
z−zmax ref
lab
− λPSi − λPSi
Otherwise,
wGOC
ref
λPSi = χlab λlab
PSi + (1 − χlab )λPSi .
4.5
4.5.1
(53a)
(53b)
Nutrients
Nitrate and ammonium
∂NO3
= Nitrif − µPNO3 P − µD
NO3 D
∂t
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O. Aumont et al.: A description of PISCES-v2
− RNH4 λNH4 1(O2 ) NH4 − RNO3 Denit
(54)
X
∂NH4
= γ Z (1 − eZ − σ Z ) g Z (I )Z + γ M (1 − eM − σ M )
∂t
I
!
X
M
M
×
g M (I ) + gFF
(POC) + gFF
(GOC) M
I
M
+ γ M Rup
+ Remin + Denit + Nfix
− µD
NH4 D
– Nitrogen fixation requires iron and phosphorus.
– Nitrogen fixation needs high light levels, i.e., Efix is
high.
m is set from the namelist and thus,
The scaling factor Nfix
may be chosen by the user.
− Nitrif − λNH4 1(O2 ) NH4
− µPNH4 P
– Nitrogen fixation is restricted to areas with insufficient
nitrogen (LPN < 0.8).
(55)
Nitrification (Nitrif) corresponds to the conversion of ammonium to nitrate due to bacterial activity. It is assumed to
be photo-inhibited (e.g., Horrigan et al., 1981; Yoshioka and
Saijo, 1984) and reduced in suboxic waters:
4.5.2
Phosphate
X
∂PO4
= γ Z (1 − eZ − σ Z ) g Z (I )Z
∂t
I
!
X
X
M
M
+ γ (1 − e − σ )
g (I ) +
gFF (I ) M
M
Nitrif = λNH4
NH4
(1 − 1(O2 )) ,
1 + PAR
PAR = PAR1 + PAR2 + PAR3 ,
I
M
+ γ M Rup
+ Remin + Denit − µP P − µD D
(59)
(56b)
All terms in this equation have been described previously.
When waters become suboxic, nitrate instead of oxygen
is consumed during the remineralization of organic matter,
i.e., denitrification (Denit). The N / C stoichiometric ratio of
denitrification RNO3 can be computed from R−O2 /NO3 and is
found to be 0.86 (Paulmier et al., 2009). Equation (57), implies that denitrification stops at oxygen concentration above
6 µM (Lipschultz et al., 1990). We further assume complete
oxidation by nitrate of the ammonia released from organic
matter during denitrification. This oxidation rate has been arbitrarily set to the same value as nitrification rate (λNH4 ).
Finally, nitrogen fixation is parameterized in PISCES as
follows:
(
0.01
if LPN ≥ 0.8
Dz
LN =
(58a)
P
1 − LN Otherwise,
(58b)
4
This very crude parameterization is based on the following assumptions that have been inferred from studies of Trichodesmium (e.g., Mills et al., 2004; Masotti et al., 2007;
Zehr, 2011):
– Nitrogen fixation is restricted to warm waters above
20 ◦ C (µP > µP (20) = 2.15).
Geosci. Model Dev., 8, 2465–2513, 2015
M
I
(56a)
where PAR is the PAR averaged over the mixed layer and
1(O2 ) varies between 0 (oxic conditions, O2 > O2 min,1 ) and
1 (anoxia) according to
!!
O2 min,1 − O2
1(O2 ) = min 1, max 0, 0.4 min,2
.
(57)
O2
+ O2
m
Nfix = Nfix
max (0, µP − 2.15) LDz
N
!
−PAR
bFe
PO4
Efix
min
, P ,min
1−e
.
Dz + bFe
KFe
KPO + PO4
M
4.5.3
Iron
P Fe,I Z
X
∂Fe
θ
g (I )
Z
IP
Z Fe,Z
= max 0, (1 − σ )
− eN θ
g Z (I )Z
Z
∂t
I g (I )
I
P Fe,I M
P
M (I )
g (I ) + I θ Fe,I gFF
Iθ
M
+ max 0, (1 − σ )
P M
P M
I g (I ) +
I gFF (I )
M Fe,Z
−eN
θ
!
X
X
M
M
M
g (I ) +
gFF (I ) M + γ M θ Fe,Z Rup
I
I
+ λ?POC SFe
Fe
Fe
− (1 − δ P )µP P − (1 − δ D )µD D − Scav−
Cgfe1 − Cgfe2 − Aggfe − Bactfe
(60)
Iron scavenging (Scav) has been described previously in
Sect. 4.4.3. Iron is present in seawater largely as colloids
(e.g., Wu et al., 2001; Wu and Boyle, 2002; Boyd and Ellwood, 2010). These colloids may aggregate with dissolved
organic matter as it forms gels. Thus, they may be transferred to the particulate pool, and settle to the ocean floor.
Very few models have incorporated this potential important
sink of dissolved iron (Ye et al., 2009, 2011). In PISCES, we
model this process following the approach chosen for DOM
(see Sect. 4.3):
Cgfe1 = ((a1 DOC + a2 POC) × sh + a4 POC
+a5 DOC) × Fecoll ,
(61a)
Cgfe2 = a3 GOC × sh × Fecoll ,
(61b)
where Fecoll is computed from the iron chemistry model (see
below).
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O. Aumont et al.: A description of PISCES-v2
2481
When dissolved iron concentration exceeds the total ligand
concentration LT , scavenging is enhanced as it is done in
many other biogeochemical models (e.g., Moore et al., 2004;
Dutkiewicz et al., 2005):
Aggfe = 1000 λFe max (0, Fe − LT ) Fe0 .
(62)
This scavenging loss term is assumed to be definitive, i.e.,
iron is permanently removed from the ocean by this process.
Heterotrophic bacteria acquire iron from seawater using
siderophore-based iron transport systems (Haygood et al.,
1993; Martinez et al., 2000). Observations show that they
have quite elevated Fe / C ratios and account for a significant
fraction of the total biological uptake of iron (Tortell et al.,
1996, 1999). The bacterial uptake of iron is parameterized
according to
Fe,Bact
Bactfe = µP LBact
lim θmax
Fe
B,1
+ Fe
KFe
Bact,
(63)
Fe,Bact
where θmax
denotes the maximum Fe / C ratio of bacteria.
The different iron pools are computed using a chemistry model. Two different chemistry models are available in
PISCES:
– A simple chemistry model based on one ligand (L) and
two dissolved iron forms: dissolved inorganic iron (Fe0 )
and dissolved complexed iron (FeL).
– The complex chemistry model of Tagliabue and Arrigo
(2006) as modified by Tagliabue and Völker (2011).
This model is based on two ligands (LW and LS ) and five
iron forms: free Fe(II) (Fe(II)0 ) and Fe(III) (Fe(III)0 ),
Fe(III) bound to the weak ligand (FeLW ), Fe(III) bound
to the strong ligand (FeLS ) and solid iron (FeP ).
The complex iron model is activated in PISCES setting the
Boolean variable ln_fechem to true.
Our main purpose is not to provide a fully detailed description of both chemistry models as they have been described fairly extensively elsewhere. For the simple chemistry model, the reader should refer to Aumont and Bopp
(2006), whereas the complex model is detailed in Tagliabue
and Völker (2011). For the complex model, all chemical constants have identical values to what was chosen in Tagliabue
and Völker (2011) and are thus not listed in Table 1a–e. Only
a very brief description of both models will be given here,
especially for the complex model. Both models are based on
the assumption that chemical reactions are fast enough relative to the other biogeochemical processes affecting iron (for
instance phytoplankton uptake) that they can be considered
at equilibrium.
4.5.4
Simple chemistry model
Dissolved iron is assumed to be in the form of free inorganic
iron Fe0 and of “complexed” iron FeL. Both forms of iron are
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assumed to be equally susceptible to consumption by phytoplankton despite recent observations suggest that this may be
not the case (Nishioka and Takeda, 2000; Chen and Wang,
2001; Chen et al., 2003). In other words, the total bioavailable concentration of iron is equal to the total dissolved iron
concentration (Fe). The chemical speciation of iron is deduced from the three following equations
LT = FeL + L0
Fe = FeL + Fe0
FeL
Fe
Keq
= 0 0.
L Fe
(64)
Fe is computed from
The chemical equilibrium constant Keq
the formulation proposed by Liu and Millero (2002). Solving this set of equations is equivalent to solve a second-order
polynomial equation in Fe0 , whose solution is
Fe
Fe
1 = 1 + Keq
LT − Keq
Fe
q
Fe Fe
−1 + 12 + 4Keq
0
.
Fe =
Fe
2Keq
(65)
Colloidal iron is assumed to represent 50 % of FeL:
Fecoll = 0.5FeL.
(66)
The total ligand concentration LT can be either constant
over the ocean, using a value defined in the namelist or can
be variable using the relationship proposed by Tagliabue and
Völker (2011):
LT = max (0.09(DOC + 40) − 3, 0.6),
(67)
where LT is in nmol L−1 and DOC in µmol L−1 .
4.5.5
Complex chemistry model
The iron chemical system is governed by the following set of
four equations
0 = klW Fe(III)0 LW − kbW FeLW − kphW FeLW
− kth FeLW ,
(68a)
0 = klS Fe(III)0 LS − kbS FeLS − kphS FeLS ,
(68b)
0 = kphW FeLW + kphS FeLS + kth Fe(III)0 − kox Fe(II)0 ,
(68c)
0
0 = kpcp Fe(III) − kr FeP .
(68d)
A supplementary reaction has been added relative to the original set of equations. In the Pacific Ocean, thermal (dark) reduction of Fe(III) organic complexes has been shown to produce the accumulation of a sizeable amount of Fe(II)0 in the
mesopelagic zone (Hansard et al., 2009).
Additional constraints are given by the conservation of total dissolved iron (Fe), LWT and LST over the fast timescale:
Fe = Fe(III)0 + Fe(II)0 + FeLW + FeLS + FeP ,
(69a)
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O. Aumont et al.: A description of PISCES-v2
LWT = FeLW + LW ,
(69b)
4.5.6
LST = FeLS + LS .
(69c)
∂Si
D,Si
= λ?PSi DissSi PSi − θopt
(1 − δ D )µD D
(74)
∂t
All terms in this equation have been already defined previously.
Solving this system of equations is equivalent to solving
a third-order polynomial equation in Fe(III)0 (Eq. 16 in Tagliabue and Völker, 2011). Because thermal aphotic reduction
of FeLW has been added here, the definition of some coefficients in the original study has changed:
kphW + kth
,
kox
kphW + kth + kbW
,
KW =
klW
b = 1+
(70a)
(70b)
where kth has been set to 0.0048 h−1 . Then, knowing Fe(III)0 ,
the other four iron species can be computed.
Observations suggest that the weak ligand (LW ) is ubiquitous in the water column and is probably produced by the
degradation of organic matter sinking from the upper layers of the ocean. The strong ligand is present in the upper
ocean and is most probably produced by autotrophic and heterotrophic bacteria (for instance siderophores) (e.g., Boyd
and Ellwood, 2010). In PISCES, we assume that two-thirds
of the total ligand concentration above 0.6 nmol L−1 is going
to LS , the rest is attributed to LW :
1
LWT = 0.6 + (LT − 0.6),
3
2
LST = (LT − 0.6).
3
(71a)
(71b)
As in the simple chemistry model, the ligand concentration
LT can be either constant over the ocean, using a value defined in the namelist or can be variable using the relationship
proposed by Tagliabue and Völker (2011) (see Eq. 67).
The rate constants required by the model are identical to
those described by Tagliabue et al. (2009a) as modified by
Tagliabue and Völker (2011). Furthermore, we have slightly
changed the formulation of the oxidation rate constant used
in the original model:
−1
0 max O2 , 1 µmol L
kox = kox
.
(72)
O2sat
This avoids numerical problems in strongly anoxic areas where oxygen concentration is close to 0. Bioavailable
iron can be defined either as Fe(II)0 + Fe(III)0 + FeLS or as
Fe(II)0 + Fe(III)0 + FeLS + FeLW . kth has assigned the value
computed from the observations by Hansard et al. (2009),
consistent with the data of Pullin and Cabaniss (2003). Colloidal iron and dissolved inorganic iron are defined as
Fecoll = 0.5(Fep + FeLW + FeLS ),
(73a)
Fe0 = Fe(III)0 + Fe(II)0 .
(73b)
We assumed that 50 % of the iron bound to ligands and of
the particulate inorganic iron is colloidal iron.
Geosci. Model Dev., 8, 2465–2513, 2015
4.6
Si
Calcite
∂CaCO3
∂CaCO3
= PCaCO3 − λ?CaCO3 CaCO3 − wGOC
∂t
∂z
(75)
In PISCES, calcium carbonate is assumed to exist only in
the form of calcite. Thus, aragonite is not considered, for instance, for the computation of chemical dissolution in the water column.
The biological production of sinking calcite is defined as
PCaCO3 = RCaCO3 ηZ g Z (P )Z + ηM g M (P )M
P
P + sh × wP P 2 ) .
(76)
+0.5(mP
Km + P
The rain ratio RCaCO3 is variable. We propose the following parameterization for this ratio:
P
T
CaCO
max 1,
RCaCO3 = rCaCO3 Llim 3
0.1 + T
2
30
max (0, PAR − 1)
×
4 + PAR
30 + PAR
−(T − 10)2
× 1 + exp
25
50
× min 1,
.
(77)
zmxl
This parameterization is based on a set of very simple assumptions, mainly inferred from the review by Zondervan
(2007):
– Coccolithophores are not very abundant in very oligotrophic waters.
– Calcification tends to be maximum at intermediate light
levels and decrease at either high and low light levels,
around 30 and 4 W m−2 , respectively.
– Coccolithophores are not found when the temperature
of sea water is below 0 ◦ C.
– Coccolithophores are found in stratified waters. Their
abundance decreases when the mixed layer depth (zmxl )
exceeds 50 m.
– Maximum levels of coccolithophores are found in the
mid-latitudes, where temperature is around 10 ◦ C.
We recognize that this parameterization is quite ad hoc and
may seem arbitrary. But as it will be shown, it simulates reasonable calcification patterns and alkalinity distribution (yet
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O. Aumont et al.: A description of PISCES-v2
2483
we recognize that it could be for the wrong reasons). Furthermore, it avoids an explicit modeling of the coccolithophores
which is far from being trivial.
Only part (ηI ) of the grazed shells are routed to sinking
calcite. The rest is taken to dissolve in the acidic guts of
zooplankton (Jansen and Wolf-Gladrow, 2001). This dissolution is still debated. However, observations tend to show
that a significant proportion of the sinking shells is lost in the
upper ocean, with this being associated with grazing as well
as other mechanisms (Milliman et al., 1999).
The dissolution of calcite is modeled as in Gehlen et al.
(2007):
!
CO2−
2−
3
,
(78)
1CO3 = max 0, 1 −
CO2−
3,sat
nca
λ?CaCO3 = λCaCO3 (1CO2−
3 ) .
4.7
X
∂DIC
= γ Z (1 − eZ − σ Z ) g Z (I )Z + γ M (1 − eM − σ M )
∂t
I
!
X
X
M
g M (I ) +
gFF
(I ) M
D
I
M
−µ D−µ P
∂Alk
?
= θ N,C Remin + θ N,C (rNO
+ 1)Denit
3
∂t
X
+ θ N,C γ Z (1 − eZ − σ Z ) g Z (I )Z
(1 − e − σ )
X
!
X
M
M M
g (I ) +
gFF (I ) M − Out
2 γ Rup
M
M
(80)
M
γ (1 − e − σ )
!
X
X
M
M
N,C M M
g (I ) +
gFF (I ) + θ γ Rup M
I
I
N,C P
N,C
+ θ µNO3 P + θ N,C µD
Nfix + 2λ?CaCO3 CaCO3
NO3 D + θ
?
+ θ N,C 1(O2 )(rNH
− 1)λNH4 NH4
4
− θ N,C µPNH4 P − θ N,C µD
NH4 D
− 2θ N,C Nitrif − 2PCaCO3
(81)
All terms in the above equations have been described previously in this document. In addition to these biogeochemical fluxes, the ocean exchanges CO2 with the atmosphere
at the sea surface. The gas exchange coefficient is computed
from the relationship proposed by Wanninkhof (1992). No
exchange is allowed with the atmosphere across sea ice:
× (1 − %ice ),
(82)
where %ice is the concentration of sea ice which varies between 0 and 1. The carbonate chemistry follows the OCMIP
protocols (more information at http://ocmip5.ipsl.jussieu.fr/
www.geosci-model-dev.net/8/2465/2015/
I
nit
− Out
2 Remin − O2 Nitrif
I
0
kgCO2 = kgCO
2
M
I
P
N,C M
Oxygen
∂O2
P
D
ut
nit
= Out
2 (µNH4 P + µNH4 D) + (O2 + O2 )
∂t
nit
(µPNO3 P + µD
NO3 D) + O2 Nfix
X
Z
Z
Z
M
− Out
g Z (I )Z − Out
2 γ (1 − e − σ )
2γ
I
M
+ γ M Rup
+ Remin + Denit + λ?CaCO3 CaCO3 − PCaCO3
+θ
4.8
(79)
The carbonate system
I
OCMIP/) except that it has been simplified to reduce the
computing cost: alkalinity only includes carbonate, borate
and water (H+ , OH− ).
Atmospheric pCO2 can be set as an external tunable parameter via a namelist parameter or read from a file. Its value
is uniform over the global ocean (no spatial gradient) and is
not allowed to vary in response to the air–sea fluxes. This
means that PISCES does not include an interactive atmospheric (box or more complex) model (although this functionality can be added very easily). Finally, the impact of atmospheric pressure on pCO2 can be accounted for by setting the Boolean ln_presatm to true in the namelist. In
that case, the 2-D spatial distribution of atmospheric pressure
should be read in a file.
(83)
In this equation, the stoichiometric ratio Out
2 represents the
change in oxygen relative to carbon when ammonium is converted to organic matter, whereas Onit
2 denotes the consumption of oxygen during nitrification. Their values have been
set respectively to 131/122 and 32/122 so that the typical
Redfield ratio for oxygen is equal to 1.34 as proposed by Kortzinger et al. (2001).
Oxygen is exchanged with the atmosphere using the parameterization of Wanninkhof (1992) to compute the gas exchange coefficient. The atmospheric concentration of oxygen
is constant over time and space and cannot be specified by
the user. As for CO2 , no air–sea fluxes are allowed when the
ocean is covered by sea ice (see Eq. 82).
4.9
External supply of nutrients
Nutrients are supplied to the ocean from five different
sources: atmospheric dust deposition, rivers, sea ice, sediment mobilization and hydrothermal vents.
4.9.1
Atmospheric deposition
The model can include the atmospheric supply of Fe, Si, P
and N. The former three sources (Fe, Si and P) are dependent
on each other as they are computed from the same dust input
file. They are activated in PISCES by setting the Boolean
ln_dust to true. Otherwise, no atmospheric source of Fe,
P and Si is prescribed. Furthermore, in that case, the dust
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O. Aumont et al.: A description of PISCES-v2
concentration in the ocean (used for instance in Eq. 50) is
set to 0. The iron content of dust is set to a constant value
specified in the namelist. Its default value is 3.5 % which
is the average content of crustal material (e.g., Taylor and
McLennan, 1985; Jickells and Spokes, 2001; Jickells et al.,
2005). The solubility of dust iron in sea water can be either
set to a constant value in the namelist or can be read from
a file if ln_solub is set to true. Once it has left the surface
layer, particulate inorganic iron from dust is still assumed to
experience dissolution. The dissolution rate is computed assuming that mineral particles sink at a constant speed specified in the namelist and that about 0.01 % of the particulate
iron dissolves in a day (Bonnet and Guieu, 2004). This is
equivalent to a remineralization length scale of 20 000 m if
the sinking speed is set to a typical value of 2 m day−1 , on
the same order as the length scale prescribed for the same
process by Moore et al. (2004). Atmospheric deposition of
Si is also considered following Moore et al. (2002b) and is
restricted to the first layer of the model. Atmospheric deposition of P is computed from dust deposition assuming that the
total phosphorus content of dust is 750 ppm (Mahowald et al.,
2008) and that the solubility in surface sea water is 10 % (Ridame and Guieu, 2002; Mahowald et al., 2008). As for Si,
deposition is restricted to the first level of the ocean model.
Atmospheric deposition of N is treated separately from the
deposition of the other nutrients and can be activated in the
model by the Boolean ln_ndepo. All nitrogen deposited at
the ocean surface is assumed to dissolve. We made the quite
strong assumption for all nutrients that sea ice does not alter
the deposition fluxes.
The dust (Dust) concentration in the ocean is modeled
in a very simplistic way in PISCES. It is computed from
dust deposition assuming a constant sinking speed (the same
as the sinking speed used to compute iron dissolution from
dust in the interior of the ocean). Furthermore, dust is not
transported by the ocean currents. This assumption is made
in PISCES to avoid adding another prognostic tracer in the
model. As a consequence, the concentration of dust is computed as
Dust =
Ddust
,
wdust
(84)
where Ddust is dust deposition at the surface and wdust is the
prescribed sinking speed of dust.
4.9.2
River discharge
River discharge is activated by setting the Boolean variable
ln_river to true in the namelist. The river discharge of the different elements is then read from a file that must be provided
in that case by the user. The river supply of DIN, DIP, DON,
DOP, Si, DIC, alkalinity and DOC need to be provided. As
DON, DOC and DOP are not separately modeled in PISCES
(fixed stoichiometry), dissolved organic matter is assumed
to remineralize instantaneously at the river mouth and thus,
Geosci. Model Dev., 8, 2465–2513, 2015
DON, DOP and DIC are added to DIN, DIP and DIC, respectively. As a default in PISCES, river supply of all elements
but DIC and alkalinity is taken from the GLOBAL-NEWS2
data sets (Mayorga et al., 2010). For DIC and alkalinity, we
use results from the Global Erosion Model (GEM) of Ludwig et al. (1996), neglecting the POC delivery as most of it is
lost in the estuaries and in the coastal zone (Smith and Hollibaugh, 1993). All fields are interpolated onto the ORCA
grid and co-localized with the river runoff prescribed in the
physical model. Iron is also delivered to the ocean by rivers.
The amount of supplied iron is computed from the river supply of inorganic carbon, assuming a constant Fe / DIC ratio.
This ratio is determined so that the total Fe supply equals
1.45 Tg Fe yr−1 as estimated by Chester (1990).
4.9.3
Reductive mobilization of iron from marine
sediments
Reductive mobilization of iron from marine sediments have
been recognized as a significant source to the ocean (Johnson et al., 1999; de Baar and de Jong, 2001; Moore et al.,
2004). Fe concentrations in the sediment pore waters are often several orders of magnitude larger than in the seawater.
A large part of the iron released to the ocean either by diffusion or by resuspension is likely to be oxidized in insoluble forms and trapped back to the sediments, at least in oxygenated waters (de Baar and de Jong, 2001). Yet, some of
this iron should escape as observations clearly show increasing concentration gradients of particulate and dissolved iron
toward the coastal zones. Unfortunately, almost no quantitative information is available to parameterize this potentially
important source. Observations from benthic chambers indicate that this source may be controlled by the oxygen concentrations overlying the sediments (Raiswell and Anderson,
2005; Severmann et al., 2010) and perhaps the magnitude
of the organic carbon export to the sediments (Elrod et al.,
2004). Such potential relationships are not yet embedded in
PISCES.
In a way similar to Moore et al. (2004), we apply a maximum constant iron source from the sediments. Since anoxic
sediments are more likely to release iron to the seawater, we
have modulated this source by a factor (Fsed) computed from
the metamodel of Middelburg et al. (1996):
z −1.5
,
(85a)
zFsed = min 8,
500 m
ζFsed = −0.9543 + 0.7662 ln(zFsed )
− 0.235(ln(zFsed ))2 ,
(85b)
Fsed = min (1, exp(ζFsed )/0.5) .
(85c)
From this metamodel, it is possible to estimate the relative contribution of anaerobic processes to the total mineralization of organic matter in the sediments, and thus
to have an indication on how well the sediment is oxygenated (Soetaert et al., 2000). Our modulation factor is simwww.geosci-model-dev.net/8/2465/2015/
O. Aumont et al.: A description of PISCES-v2
2485
ply set equal to this relative contribution. The maximum
iron flux from the sediments has been set by default to
2 µmol Fe m−2 d−1 by adjusting the modeled iron distribution
to the few iron observations available over the continental
margins. This value is identical to that used by Moore et al.
(2004) in their model. The maximum iron flux constant can
be specified in the namelist and thus, may be changed from
the default value by the user.
Unfortunately, as a consequence of the relatively coarse
resolution of ORCA2, the model bathymetry is not able to
correctly represent the critical spatial scales of the ocean
bathymetry. An example is the continental shelves, which
typically have a width scale of 10–30 km, which can be approximately an order of magnitude less than the horizontal
resolution of the model. In order to take sub-model grid scale
bathymetric variations into account in the Fe source function,
the model grid structure has been compared with the highresolution ETOPO5 data set. An algorithm was developed
whereby for each and every horizontal grid cell, the corresponding region in the ETOPO5 data set is considered. For
each vertical level in the model corresponding to a particular
horizontal grid point, the corresponding ocean-bottom area
from ETOPO5 (in fractional units) is saved, with the end result being a three-dimensional array containing an equivalent
area for the bottom bathymetry of the ocean for the ETOPO5
data set. The iron flux computed as described above is then
multiplied by this fractional area %sed (which varies between
0 and 1):
sed
sed
FFe
= FFe,max
× Fsed × %sed .
(86)
This corresponds to a global flux of 34 Gmol Fe yr−1 .
4.9.4
Iron from hydrothermalism
Recent studies have shown that hydrothermalism may deliver to the deep ocean a significant amount of dissolved iron
(e.g., Mackey et al., 2002; Boyle and Jenkins, 2008; Bennett et al., 2008; Toner et al., 2009). Despite very large uncertainties, this source has been estimated, based on discrete
data and a model, to 3 to 9 × 108 mol Fe yr−1 globally (Bennett et al., 2008; Tagliabue et al., 2010). In PISCES, this
source is included following the modeling study by Tagliabue
et al. (2010) and may be activated by setting the Boolean
ln_hydrofe to true. The hydrothermal flux of iron has
been computed based on observed correlations between 3 He
and dFe (Boyle et al., 2005; Boyle and Jenkins, 2008) and using a data compilation of dFe / 3 He (see the Supplement of
Tagliabue et al., 2010). Then, the spatial distribution of this
flux has been derived from previous modeling works on 3 He,
which relate the 3 He flux to the ridge-spreading rates (Farley
et al., 1995; Dutay et al., 2004); 0.2 % of the delivered iron
is assumed to be soluble.
www.geosci-model-dev.net/8/2465/2015/
Si
Si,D
D . The
Figure 3. θopt
as a function of Si concentration and Flim,1
vertical axis corresponds to log(Si).
4.9.5
Iron from sea ice
The last external source of nutrients which is taken into
account in PISCES is the exchange of iron between the
ocean and the sea ice associated with formation and melting. This source is activated by setting the Boolean variable ln_ironice to true. The receding ice edge is often
characterized by intense phytoplankton abundance which can
be explained by ocean stratification promoted by the melting of sea ice (Smith and Nelson, 1985) as well as the releases of iron accumulated in sea ice during winter (Sedwick and Di Tullio, 1997; Tagliabue and Arrigo, 2006). Measurements in sea ice have found iron concentrations of more
than 1 order of magnitude higher than in adjacent sea water (Lannuzel et al., 2007, 2008). About 90 % of this iron has
been shown to be of oceanic origin (Lannuzel et al., 2007).
Thus, iron is taken up from sea water when ice forms and
is released back to the ocean when it melts. Lancelot et al.
(2009) have studied the impact of this source in the Southern
Ocean and shown that it is of primary importance in the seasonal ice zone. Their approach relies on the modeling of iron
concentration within sea ice. In PISCES, we have simplified
this model by assuming that iron concentration in sea ice is
constant. In that case, the iron fluxes between the ocean and
the sea ice can be computed from the water fluxes between
these two reservoirs:
ice,−
FFe
= min (0, −EPoi ) × Fe,
(87a)
ice,+
FFe
= max (0, −EPoi ) × Feice ,
ice,−
ice,+
ice
= FFe
+ Fice
,
FFe
(87b)
(87c)
where EPoi is the water flux (in kg m−2 s−1 ) from the ice
to the ocean and Feice is the iron concentration in sea ice
which has been found to be on the order of 10 nmol L−1 . In
ice,−
this equation, FFe
is thus the loss of iron from the ocean
ice,+
when sea ice forms and FFe
is the release of iron to ocean
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the proportion of degradation of the remaining organic matter
that is due to denitrification:
log(Pdenit ) = − 2.2567 − 1.185 log(FOC ) − 0.221(log(FOC ))2
− 0.3995 log(NO3 ) log(O2 )
+ 1.25 log(NO3 ) + 0.4721 log(O2 )
− 0.0996 log(z)
+ 0.4256 log(FOC ) log(O2 ),
Figure 4. Dissolution rate of PSI (λ?PSi ) normalized to its value at
0 ◦ C with no silicate. Temperature is in ◦ C.
when sea ice melts. It should be noted here that since we
do not model iron in sea ice, the exchange of iron between
both reservoirs is not conservative. In the model configuration presented here, ice represents a net source of iron of
0.024 Gmol Fe yr−1 .
4.10
Bottom boundary conditions
At the bottom of the ocean, the exchange between the sediments and the ocean can be represented either with or without
a sediment model. The sediment model is activated by using
the cpp key key_sed. This model will not be described in
this document. It is basically identical to the model of Heinze
et al. (1999) with some modifications as described by Gehlen
et al. (2006). The main modification is the addition of denitrification to the set of early diagenetic reactions. Parameter
values are identical to those in Heinze et al. (1999).
When the sediment model is not activated, very basic but
different treatments are applied at the bottom of the ocean
depending on the tracer considered. For biogenic silica, the
amount of particulate material that is permanently buried in
the sediments is assumed to exactly balance the external input from dust deposition and river discharge, described in the
previous section. Then, we assume that the part of biogenic
silica that is not permanently buried redissolves back to the
water column instantaneously.
For particulate organic carbon, we first determine the proportion of organic matter reaching the seafloor that is permanently buried. The burial efficiency is computed using the
algorithm proposed by Dunne et al. (2007):
Eburial = 0.013 +
2
0.53FOC
,
(7.0 + FOC )2
(88)
where Eburial is the burial efficiency and FOC is the flux of
organic carbon at the bottom (in mmol C m−2 d−1 ). We then
use the metamodel by Middelburg et al. (1996) to determine
Geosci. Model Dev., 8, 2465–2513, 2015
(89)
where the tracer concentrations are in µmol L−1 and FOC is
the flux of organic carbon at the bottom (in µmol cm−2 d−1 ).
In this equation, oxygen and nitrate concentrations are not
allowed to be below 10 µmol L−1 and 1 µmol L−1 , respectively. Then, the fluxes of nitrate and oxygen to the sediment
as a consequence of denitrification and oxic degradation, respectively, can be computed:
denit
FNO
= RNO3 Pdenit FOC ,
3
(90a)
FOoxic
= Out
2 (1 − Pdenit ) FOC .
2
(90b)
Particulate organic carbon which has been degraded by
denitrification and oxic processes is released in the bottom
box as ammonium.
A specific treatment of calcite at the sediment interface
is embedded in PISCES. The preservation of calcite in the
sediments is represented as a function of the saturation level
of the overlying waters:
0.2 − 
,
(91)
%CaCO3 = min 1, 1.3
0.4 − 
where  is the calcite saturation level. This relationship has
been deduced from the study by Archer (1996). The permanent burial of calcite is modulated by %CaCO3 . The amount
of calcite that is not buried, instantaneously dissolves back to
the ocean.
5
Model parameters and their default values
Table 1a–e list model parameters, their respective units and
default values as well as a brief description of each of
them. Many of these parameters can be specified in the
namelist_pisces file. As much as possible, the parameter values have been derived from the literature. However,
many parameters, such as the mortality rates, are either not
constrained at all, or only poorly constrained by the observations. Their values have been adjusted by successive simulations evaluated against the observational data sets presented
below.
In addition to the parameters above, PISCES includes
a number of control parameters defined as Boolean variables
that appear in the namelist file namelist_pisces. These
variables either allow one to switch between different functional forms or activate additional functionalities. These conwww.geosci-model-dev.net/8/2465/2015/
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2487
Table 2. Boolean variables in the namelist. These variables activate functionalities of PISCES.
Boolean name
Description
ln_co2int
ln_presatm
ln_varpar
ln_newprod
ln_dust
ln_solub
ln_river
ln_ironsed
ln_ironice
ln_hydrofe
ln_pisdmp
ln_check_mass
Read atmospheric pco2 from a file (T) or constant (F)
Constant atmospheric pressure (F) or from a file (T)
PAR made a variable fraction of shortwave (T) or not (F)
Use Eq. (2a) (T) or Eq. (2b) for phytoplankton growth
Dust input from the atmosphere (T)
Variable solubility of iron in dust (T)
River discharge of nutrient (T)
Sedimentary source of iron (T)
iron input from sea ice (T)
iron input from hydrothermalism (T)
Relaxation of some tracers to a mean value (T) ∗
Check mass conservation (T)
∗ The frequency at which the restoring technique is applied is specified by the parameter nn_pisdmp.
Table 3. Available CPP keys in PISCES.
CPP Key
Description
key_pisces
key_kriest
key_sed
Activate the PISCES model
Activate the Kriest model (see Sect. 4.4)
Activate the sediment model (see Sect. 4.10)
trol parameters are listed in Table 2. Finally, some functionalities, such as the Kriest model of particulate organic matter, require a major reorganization of the code, for instance
a change in the number of prognostic variables. In that case,
these functionalities are activated through CPP keys which
force the model to be recompiled. These CPP keys are listed
in Table 3.
6
Model results
The objective of this section is not to present a full and exhaustive validation of the model results. This has already
been presented in a wide range of publications using different configurations of the model (see the Introduction).
Here we present instead a brief comparison of PISCES with
available observations, in its standard global configuration.
This configuration is the default setup available when downloading the code from the NEMO web site (the standard
ORCA2_OFF_PISCES configuration). All the necessary input files can be obtained from this web site.
6.1
Model setup
The dynamical state of the ocean has been simulated using the ocean physical model ORCA2-LIM in version 3.2
(Madec, 2008). This model is based on an ocean general
circulation model OPA9, coupled with the sea ice model
Louvain-la-Neuve Ice Model (LIM2) (Timmermann et al.,
2005). The spatial resolution is about 2◦ by 2◦ cos 8 (where
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8 is the latitude) with a focusing of the meridional resolution
to 0.5◦ in the equatorial domain. The model has 30 vertical
layers, with an increased vertical thickness from 10 m at the
surface to 500 m at 5000 m. Representation of the topography
is based on the partial step thicknesses (Barnier et al., 2006;
Penduff et al., 2007). Lateral mixing along isopycnal surfaces
is performed both on tracers and momentum as in Lengaigne
et al. (2003). The parameterization of Gent and McWilliams
(1990) is applied poleward of 10◦ to represent the effects of
non-resolved mesoscale eddies. Vertical mixing is parameterized using the turbulent kinetic energy (TKE) scheme of
Gaspar et al. (1990), as modified by Madec (2008).
The fields used to drive the ocean are identical to those
used by Aumont and Bopp (2006). However, the resulting
physical circulation state simulated by the ocean model is
different as several new parameterizations and new algorithms have been included in ORCA2-LIM. Climatological
atmospheric forcing fields have been constructed from various data sets consisting of daily NCEP/NCAR 2 m atmospheric temperature averaged over 1948–2003 (Kalnay et al.,
1996), monthly relative humidity (Trenberth et al., 1989),
monthly ISCCP total cloudiness averaged over 1983–2001
(Rossow and Schiffer, 1999), monthly precipitation averaged
over 1979–2001 (Xin and Arkin, 1997) and weekly wind
stress based on European Remote-Sensing Satellite (ERS)
satellite product and TAO observations (Menkes et al., 1998).
Surface heat fluxes and evaporation are computed using empirical bulk formulas as described by Goose (1997). To avoid
any strong model drift, modeled sea surface salinity is restored to the monthly WOA01 data set (Conkright et al.,
2002) with a nudging timescale of 40 days applied through
local freshwater forcing (thereby conserving salt). The ocean
dynamical model has been spun-up for 200 years, starting
from rest and from the climatology of Conkright et al. (2002)
for temperature and salinity.
Phosphate, oxygen, nitrate and silicic acid distributions
have been initialized at uniform concentrations inferred from
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Table 4. Global annual budget of C in the top 150 m of the ocean.
Carbon budget a
Primary production in the top 150 m of the ocean
7.5
36.8
44.3
Primary production by diatoms
Primary production by nanophytoplankton
Global total primary production
Export from the top 150 m of the ocean
3.9
2
1
6.9 b
Vertical flux due to sinking big POC
Vertical flux due to sinking small POC
Advective/diffusive vertical flux of organic matter
Total vertical flux of organic matter
Various fluxes in the top 150 m of the ocean
35.8
40.2
4
11.2
51.2
22.3
Grazing by microzooplankton on phytoplankton
Total grazing by microzooplankton
Grazing by mesozooplankton on phytoplankton
Total grazing by mesozooplankton
Total grazing by zooplankton
Remineralization of DOC
a Carbon fluxes are all in Gt C yr−1 . b The total vertical flux due to sinking POC is
7.3 Gt C yr−1 at 100 m depth.
observed climatologies (Garcia et al., 2010). Initial values
for dissolved inorganic carbon and alkalinity are taken from
the OCMIP guidelines (Orr, 1999). The ecological tracers
are initialized uniformly to arbitrary low values. Iron concentrations are set everywhere to 0.6 nM. The model is then
spun-up offline for 4000 years using the circulation state predicted by the dynamical model. Atmospheric pCO2 is set to
a pre-industrial value of 278 ppm. After this integration, primary productivity as well as CO2 fluxes drift by less than
0.001 Gt C yr−1 . As the external sources and sinks of nutrients are not fully balanced (see the model description), the
global inventories of phosphate, nitrate, alkalinity and silicate are restored toward the observed inventories, once a year
on 1 January. In practice, this correction is done by scaling
the 3-D concentrations with a constant uniform factor so that
the simulated total inventories do not drift away from the observed inventories. Thus, we do not restore the simulated 3-D
distributions to 3-D observed fields so that the predicted spatial and temporal patterns are not corrected in any way to better match the observations. However, the predicted global inventories of P, N, Si and alkalinity can not be used to evaluate
the model skill since they are not prognostically predicted.
Anyhow, this correction is very small and corresponds to a
relative change in the concentration of the tracers on the order of 1–5 × 10−5 yr−1 ; therefore, that no significant jump is
introduced by this technique. The activation of this technique
as well as the frequency at which it is applied are controlled
by a Boolean parameter and a parameter respectively, in the
namelist file namelist_pisces (see Table 2).
Geosci. Model Dev., 8, 2465–2513, 2015
6.2
Global budget
Table 4 presents the global carbon budget as simulated by
PISCES, when embedded in ORCA2-LIM. The annual net
predicted primary production is 44 Gt C yr−1 . This value falls
on the lower bound of the broad estimates given by satellite
observations which give values between 37 and 67 Gt C yr−1
(Longhurst et al., 1995; Antoine et al., 1996; Behrenfeld and
Falkowski, 1997; Behrenfeld et al., 2005). Using PISCES in
a higher resolution model would certainly produce a significantly larger number as mesoscale and submesoscale processes have been shown to stimulate biological productivity
(McGillicuddy et al., 1998; Oschlies and Garçon, 1998; Lévy
et al., 2001), and coastal regions, characterized by a intense
primary productivity, are not properly resolved by the coarse
grid.
About 17 % of the primary production is due to diatoms.
Global estimates of the contribution of diatoms to total production are rather uncertain and broad. Nelson et al. (1995)
have suggested that diatoms may be responsible for up to
40 % of the total primary production. However, as discussed
by Aumont and Bopp (2006), this value is certainly overestimated. In recent years, algorithms, which attempt to retrieve
the composition of phytoplankton from space, have been developed (e.g., Alvain et al., 2005; Uitz et al., 2006; Hirata
et al., 2008; Brewin et al., 2010). Only a few of these methods
give quantitative estimates of the contribution of the different
species or size classes to total biomass or primary productivity (Brewin et al., 2011). The estimated global contribution
of diatoms from these methods ranges from as low as 7 %
to as high as 32 % of the total phytoplankton (Uitz et al.,
2010; Hirata et al., 2011) (if one assumes crudely that microphytoplankton are effectively equivalent to diatoms). Finally, ocean biogeochemical models predict the contribution
of diatoms to be between 15 and 30 % (e.g., Moore et al.,
2002a; Aumont et al., 2003; Dutkiewicz et al., 2005; Yool
et al., 2011).
Export production at 150 m is estimated to be
6.9 Gt C yr−1 ; 86 % of this export is related to settling
particles (one-third by the small sinking particles and twothird by the fast sinking particles). The remainder is due to
vertical advection and diffusion of dissolved organic carbon,
which occurs mainly in the mid-ocean gyres (vertical advection) and in the high latitude regions during winter (vertical
diffusion). Constraining export production is rather difficult,
if not impossible, considering the very broad range given
by estimates either based on models or observations and
the different definitions of export production, in particular
the depth horizon at which it is estimated (e.g., Eppley and
Peterson, 1979; Schlitzer, 2000; Moore et al., 2002a; Yool
et al., 2011). Mesozooplankton grazes about 9 % of total
primary production. This value is close to other estimates
either based on observations (Calbet, 2001) or models
(Moore et al., 2002a; Buitenhuis and Geider, 2010). Total
gazing by mesozooplankton is predicted to be 11.2 Gt C yr−1
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Table 5. Global annual budget of calcite and Si in the top 150 m of
the ocean.
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Table 6. Annual budget∗ of N over the global ocean.
Sources of nitrogen to the ocean
Calcite budgeta
1.6
0.8
0.8
36
67
111.8
Production of calcite
Dissolution of calcite
Vertical flux of sinking calcite particles
214.8
Biogenic silica budgetb
145.8
39.6
106.2
River discharge
Atmospheric deposition
Nitrogen fixation
Total input of nitrogen
Sinks of nitrogen from the ocean
Production of BSi
Dissolution of BSi
Vertical flux of dissolved BSi
77.6
92.8
23.2
a Calcite fluxes are all in Gt C yr−1 . b Biogenic silica fluxes are all in
Tmol Si yr−1 .
193.6
Denitrification in the water column
Denitrification in the sediments
Permanent burial in the sediments
Total loss of nitrogen
21.2
Net budget of nitrogen (Sources minus Sinks)
∗ All nitrogen fluxes are in Tg N yr−1 .
by PISCES, quite similar to the value of 10.4 ± 3.7 Gt C yr−1
estimated by Hernández-León and Ikeda (2005) for the
global respiration of mesozooplankton in the upper 200 m
of the ocean. About 80 % of total primary production, i.e.,
35.8 Gt C yr−1 , is consumed up by microzooplankton above
the upper bound of the 25–33 Gt C yr−1 given by Buitenhuis
et al. (2010) when extrapolating observations. Despite
estimates of grazing by microzooplankton are quite badly
constrained, this might suggest that it is overestimated in the
model.
Table 5 shows the calcite and silicon budgets for the upper
150 m of the ocean. Production of calcite and export at 150 m
are simulated to be, respectively, about 1.6 and 0.8 Gt C yr−1
by PISCES. These numbers fall within the limits of the
quite large range of 0.4–1.8 Gt C yr−1 estimated either for
global calcification or export of particulate inorganic carbon
(PIC) (Murnane et al., 1999; Lee, 2001; Moore et al., 2002a;
Balch et al., 2007; Berelson et al., 2007). For silicate, the
model predicts a vertical export of biogenic silicate of 106
Tmol Si yr−1 . This value is within the 105 ± 17 Tmol Si yr−1
estimated for the global ocean (Tréguer and De La Rocha,
2012). Global production of biogenic silica by diatoms is
146 Tmol Si yr−1 in our model. This value is quite low compared to the 239 Tmol Si yr−1 given by Tréguer and De La
Rocha (2012). About 27 % of biogenic silica dissolves in the
top 150 m of the ocean, half the estimate of Nelson et al.
(1995) and Tréguer and De La Rocha (2012). However, as already mentioned, because of its coarse resolution, the physical model configuration does not properly resolve the coastal
zones. For the open ocean only (in a strict sense), Tréguer and
De La Rocha (2012) estimated biogenic silica production to
be about 103 Tmol Si yr−1 . Not surprisingly then, considering the limitations due to the spatial resolution, our modeled
estimate is between the open ocean and global values. The
mean Si / C for uptake of diatoms as predicted by PISCES is
thus 0.23, which is high relative to the optimal Si / C of 0.13
(Brzezinski, 1985). This suggests thus that over most of the
ocean, diatom cells are stressed, not a very surprising result.
Furthermore, a large part of the biogenic silica production ocwww.geosci-model-dev.net/8/2465/2015/
curs within the Southern Ocean, a region where diatom cells
are very heavily silicified (Baines et al., 2010).
Table 6 presents the global nitrogen budget as simulated by PISCES. River discharge and atmospheric deposition of nitrogen are given by the prescribed input fields to
PISCES. By definition, burial in the sediments is set exactly
equal to river discharge. Nitrogen fixation is predicted to
be 111.8 Tg N yr−1 . This value is close to the mean value
of about 140 Tg N yr−1 estimated from direct observations
or nutrients analysis (Capone et al., 1997; Deutsch et al.,
2007). Figure 6 shows a comparison between the spatial distribution of observed nitrogen fixation rates from the MARine Ecosystem DATa (MAREDAT) project and that as simulated by PISCES. This indicates that, despite a quite simplistic formulation, the model is able to capture the main
observed patterns, at least on an annual-mean basis. Modeled denitrification in the water column and in the sediments
are about 78 and 93 Tg N yr−1 , respectively. Sediment denitrification estimates are significantly higher, in the range of
130–300 Tg N yr−1 (Codispoti et al., 2001; Galloway et al.,
2004; Gruber, 2004). However, considering the coarse spatial resolution of the model, this is expected as most of benthic denitrification occurs over the continental margins. The
sources and sinks of nitrogen are slightly unbalanced, with
the sources exceeding the sinks by about 21 Tg N yr−1 .
6.3
6.3.1
Modeled tracer distributions
Chlorophyll
The modeled chlorophyll distribution is compared to GLOBCOLOUR satellite observations for two seasons in Fig. 7.
The seasons have been defined to roughly correspond to
bloom periods in the high latitudes. The observed patterns
are qualitatively reproduced by the model. Slightly too low
chlorophyll concentrations are simulated in the subtropical gyres. This discrepancy may be explained by the lack
of acclimation dynamics to oligotrophic conditions in the
model or by the assumption of constant stoichiometry eiGeosci. Model Dev., 8, 2465–2513, 2015
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Figure 5. Sediment source of iron as a function of depth. This plot
displays the vertical variation of Fsed (see Eq. 85 for the definition
of this factor).
ther in phytoplankton or in organic matter (Ayata et al.,
2013). Chlorophyll concentrations are quite strongly underestimated in the equatorial Atlantic and in the Arabian Sea. In
the latter region, mesoscale and submesoscale processes have
been shown to be of critical importance (Lee et al., 2000;
Kawamiya, 2001; Hood et al., 2003). A model study, using
PISCES coupled to a higher resolution version of NEMO,
has been shown to simulate chlorophyll distribution in much
better agreement with the observations (Koné et al., 2009).
Chlorophyll concentrations are high in the eastern boundary upwelling systems. The sedimentary source of iron plays
a critical role in these systems. When this iron source is not
included in models, modeled chlorophyll concentrations are
much lower (Aumont and Bopp, 2006; Moore and Braucher,
2008).
In two of the three main HNLC regions, i.e., the equatorial
Pacific and the eastern subarctic Pacific, the model succeeds
in reproducing the moderate chlorophyll concentrations. In
spring, chlorophyll levels are strongly overestimated east of
Japan. As in all coarse resolution models, the ocean circulation in this region is not correctly represented with an incorrect trajectory of the Kuroshio current (i.e., Gnanadesikan
et al., 2002; Dutkiewicz et al., 2005; Aumont and Bopp,
2006). Simulated mixed layer depths are too deep in winter
and as a consequence the spring bloom is very strong (similar features occur in the North Atlantic). In the equatorial
Pacific Ocean, a minimum threshold value has been imposed
on iron (0.01 nmol L−1 ) in the model. If not used, chlorophyll concentrations become much too low on both sides of
the Equator, resulting in an accumulation of macronutrients
and a poleward migration of the southern (northern) boundary of the northern (southern) subtropical gyre (see Fig. 5 in
Tagliabue et al., 2009a). The existence of such a threshold
suggests that either a minor but regionally important source
Geosci. Model Dev., 8, 2465–2513, 2015
Figure 6. Annual-mean depth averaged N2 fixation rates in
µmol N m−2 d−1 . (a) Database from the MARine Ecosystem Model
Intercomparison Projec (MAREMIP) project (Luo et al., 2013); (b)
model predictions.
of iron is missing in PISCES (for instance the dissolution of
particulate inorganic iron) or that the standard iron chemistry
is too simple (Tagliabue et al., 2009a; Tagliabue and Völker,
2011).
In the Southern Ocean, the third and largest of the principal HNLC regions, chlorophyll concentrations appear to
be strongly overestimated by the model when evaluated
against satellite-derived observational products, especially
during summer. Furthermore, the increase in phytoplankton
in late spring and early summer occurs too early. However,
numerous studies comparing satellite chlorophyll to in situ
data have shown that the standard algorithms used to deduce
chlorophyll concentrations from reflectance tend to underestimate in situ observed values by a factor of about 2 to 2.5,
especially for intermediate concentrations (e.g., Dierssen and
Smith, 2000; Korb et al., 2004; Garcia et al., 2005; Kahru and
Mitchell, 2010). Clearly, evaluating the model in the Southern Ocean is quite challenging and requires a more thorough
systematic analysis of both the model and the available data
sets.
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Figure 7. Surface seasonal mean chlorophyll concentrations (mg chl a m−3 ) in April-May-June (panels a and c) and November-DecemberJanuary (panels b and d). Panels (a) and (b) display satellite observations from GLOBCOLOUR. Panels (c) and (d) are model results.
6.3.2
Iron
Figure 8 shows the distribution of iron at three different
depth ranges for the model and for the observations. The observational distributions come from the recently published
database of Tagliabue et al. (2012) augmented with about
1000 recent observations. The data set can be downloaded
from http://pcwww.liv.ac.uk/~atagliab. A complete and exhaustive validation of the model is made difficult by the relative sparsity of the data.
As expected, the highest concentrations of iron in the open
ocean are found in the subtropical North Atlantic Ocean and
in the Arabian Sea. Those high values are produced by the
enhanced dust deposition, mainly emanating from the Sahara desert. The model tends to underestimate the maximum values found in both basins. Interestingly, the local
minimum, which is observed west off Mauritania just below the maximum Saharan dust plume, is well captured by
the model. Such a minimum is explained by the combination of very low solubilities of the iron contained in the
Saharan dust particles when they are close to their source
region (Bonnet and Guieu, 2004; Luo et al., 2005) with enhanced scavenging by the dust particles deposited at the
ocean surface (Wagener et al., 2010). Very high iron concentrations, typically above 1 nmol L−1 are both observed and
modeled along the coasts and over the continental margins
as a result of sediment mobilization. As already mentioned
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in the previous section, this strong source of iron sustains the
high productivity observed along the coasts (Johnson et al.,
1999), in the eastern boundary upwelling systems (Bruland
et al., 2005) but also downstream of the islands, especially in
the Southern Ocean (Blain et al., 2007; Pollard et al., 2007;
Korb et al., 2008). In the rest of the open ocean, iron concentrations are typically low, generally below 0.2 nmol L−1 ,
especially in the HNLC regions. PISCES tends to exaggerate
these low concentrations.
Iron concentrations increase with depth due to the remineralization of organic particles settling from the surface
waters (Johnson et al., 1997; Moore and Braucher, 2008).
However, except near the coasts, concentrations rarely exceed 1 nmol L−1 . Again, PISCES captures the main observed
patterns both at intermediate depths and in the deep ocean.
In the Atlantic Ocean and in the Arabian Sea, iron concentrations remain relatively elevated at intermediate depth
in the observations and in the model. In the model, these
high values are due to the slow but significant release of
iron by the dust particles which sink out from the surface.
In the Pacific Ocean, the coastal signature extends far beyond the coastal domain. For instance, it has been proposed as a potential explanation for the episodic blooms
observed at station P in the northeastern subarctic Pacific
Ocean (Lam et al., 2006; Misumi et al., 2011). In the deepest waters of the Pacific and Indian oceans, iron concentra-
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Figure 8. Spatial distribution of annual-mean iron concentrations (in nmol L−1 ) as observed (left column) and as simulated by PISCES
(right column). On panels (a) and (b), iron has been averaged over the top 50 m of the ocean. On panels (b) and (c), iron has been averaged
over 200–1000 m. The bottom two panels display the iron distributions average over the depth range 1000–5000 m. Model values have been
sampled at the same location and month as the data.
tions tend to decrease to the bottom of the ocean and they
often fall below 0.6 nmol L−1 . Despite the fact that ligands
concentrations in seawater are highly variable, they are typically larger than this value which is the uniform ligand concentration chosen in the model experiment shown here (e.g.,
Wu and Luther, 1995; Boyé et al., 2001, 2003; Hunter and
Geosci. Model Dev., 8, 2465–2513, 2015
Boyd, 2007; Ibisanmi et al., 2011). The model explains this
decrease by the aggregation of iron colloids which are transferred to the particulate pool and thus sink out of the ocean
as hypothesized by several studies (Wu et al., 2001; Ye et al.,
2009; Geldhill and Buck, 2012). The lowest iron concentrations in the intermediate and deep ocean are found in the
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Figure 9. Annual-mean NO3 concentrations in µmol N L−1 . Observations are from the World Ocean Atlas 2009 (Garcia et al., 2010).
(a) Observed surface. (b) Model run surface. (c) Observed transect zonally averaged over the Atlantic. (d) Same as (c) but for the
model. (e) Observed transect zonally averaged over the Pacific. (f)
Same as (e) but for the model.
Southern Ocean. Iron concentrations slowly increase with
depth to reach about 0.4 nmol L−1 in the deep ocean. Higher
values are found along Antarctica due to sediment mobilization.
6.3.3
Nutrients, oxygen, alkalinity and DIC
In this section, the simulated distributions of macronutrients,
oxygen, alkalinity and DIC are evaluated against available
observations. The observations comprise the World Ocean
Atlas 2009 for nutrients and oxygen (Garcia et al., 2010),
and the GLobal Ocean Data Analysis Project (GLODAP)
database for DIC and alkalinity (Key et al., 2004).
Figures 9 and 10 show the surface distributions of nitrate
and silicate and zonally averaged sections in the Atlantic and
Pacific oceans. At the surface, the model compares quite well
with the observations, especially for nitrate. Nitrate concentrations seem to be slightly overestimated along the Antarctic
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2493
Figure 10. Annual-mean SiO3 concentrations in µmol Si L−1 . Observations are from the World Ocean Atlas 2009 (Garcia et al.,
2010). Panels are the same as on Fig. 9.
coast. However, as most of the data have been collected during the productive season in this region, the climatology is
likely to be biased toward low values. The surface silicate
distribution is less well represented by PISCES, in particular in the Southern Ocean. The silicate front (defined as the
latitude at which silicate becomes exhausted) is located too
far north in the model. At depth, both modeled nutrients exhibit the same deficiencies. In the Atlantic Ocean, concentrations in the deep ocean are strongly overestimated. Too shallow North Atlantic deep waters (NADW), with strongly underestimated transport simulated for lower NADW, accounts
for this problem (Arsouze et al., 2008; Griffies et al., 2009;
Smith et al., 2010). As a result, Antarctic bottom waters,
characterized by high silicate and nitrate concentrations, tend
to dominate over too large part of the deep Atlantic Ocean.
In the Pacific Ocean, both nitrate and silicate concentrations
are underestimated in the deep waters of the Northern Hemisphere.
In Fig. 11, the modeled oxygen distribution is evaluated
against observations. Not surprisingly, the surface distribution compares quite well to the observations as oxygen is
Geosci. Model Dev., 8, 2465–2513, 2015
2494
Figure 11. Annual-mean O2 concentrations in µmol L−1 . Observations are from the World Ocean Atlas 2009 (Garcia et al., 2010).
Panels are the same as on Fig. 9.
close to its solubility value and is thus strongly constrained
by sea surface temperature. At depth, the main deficiency
is the overestimation of oxygen concentrations in the Pacific Ocean. Ventilation along Antarctica, mainly in the Ross
and Weddell seas, is too strong in the physical model. Inspection of the simulated mixed layer depths shows that the
mixed layer reaches the bottom of the ocean at several locations along Antarctica (not shown), which is not realistic
(de Boyer-Montégut et al., 2004). The nearly homogeneous
oxygen concentrations south of 60◦ S are a consequence of
this too intense winter mixing, which thus ventilates the deep
ocean with too much oxygen.
Figures 12 and 13 display the modeled and observed distributions of DIC and alkalinity at the surface and along
zonally averaged sections in both the Atlantic and the Pacific. Modeled DIC does not include the anthropogenic perturbation since atmospheric CO2 was set to its pre-industrial
value. We have estimated the observed pre-industrial distribution of DIC as the difference between total DIC and anthropogenic carbon, which are both available in GLODAP
Key et al. (2004). It should be also mentioned here that no
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Figure 12. Annual-mean natural DIC concentrations in µmol L−1 .
Observations are from GLODAP. The pre-industrial distribution of
DIC has been estimated in GLODAP as the difference between total
DIC and anthropogenic carbon. Panels are the same as on Fig. 9.
observations were available north of 60◦ N. Values north of
this latitude have been extrapolated for plotting purpose. At
the surface, several modeled features are not visible in the
observations. Very low alkalinity and DIC concentrations are
predicted in the Bay of Bengal, in the Gulf of Guinea, close
to the Indonesian islands and generally at the mouths of the
tropical rivers. The lack of observations in these regions may
explain this difference, as the GLODAP database is based
on a rather coarse sampling coverage. In the deep ocean, the
main deficiencies noticed for the macronutrients are apparent
in the simulated distributions.
6.4
Skill assessment
In this section, we quantitatively estimate the model performance using Taylor diagrams (Taylor, 2001). Taylor diagrams evaluate both the correlation normalized by the observed standard deviation (SD) (circumference axis) and the
relative variability (radial axis) of the model and observations. The distance between the model points and the (1,1)
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Figure 14. Taylor diagrams of model–observation comparisons for
surface chlorophyll (log10-transformed) using monthly mean fields
(a) and annual-mean fields (b). Black dot corresponds to global
comparison; red dot to the Atlantic Ocean, green dot to the Pacific
Ocean, brown dot to the Indian Ocean and gray dot to the Southern
Ocean (south of 45◦ S).
Figure 13. Annual-mean alkalinity concentrations in µmol eq L−1 .
Observations are from GLODAP. Panels are the same as on Fig. 9.
coordinate point (defined as the reference point) is equal to
the standard root mean error, normalized by the observed SD.
The closer the model is to the observations, the closer the
points should be to the reference point. Although a number
of means and diagnostics exist (Allen et al., 2007; Doney
et al., 2009; Vichi and Masina, 2009), Taylor diagrams have
become quite popular as they synthesize, in a quite convenient way, several statistical diagnostics.
Figures 14 and 15 show Taylor diagrams for surface
chlorophyll and mesozooplankton averaged over the top
150 m of the ocean. The agreement is rather modest for both
variables, especially for mesozooplankton. For chlorophyll,
the model performs slightly better for annual-mean distributions, which suggests biases in the representation of the seasonal cycle. The Southern Ocean exhibits the poorest agreement. In particular, the model tends to strongly underestimate
the spatial variability since the SD is smaller for the annualmean distribution than for seasonally varying fields. In the
other basins, the variability is overestimated, especially in
the Atlantic Ocean where the spring blooms in the subarctic
domain are too intense, at least relative to satellite observations (see Fig. 7). Mesozooplankton variability is strongly
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underestimated by PISCES in all basins. The use of a square
closure scheme for mortality may partly explain this bias
as this scheme tends to dampen extremes. Preliminary tests
with PISCES coupled to the upper trophic layer model Apex
Predators ECOSystem Model (APECOSM) (Maury et al.,
2007) produce a much greater spatial and temporal variability for mesozooplankton, especially in the high latitudes and
along the continental margins.
Figure 16 shows Taylor diagrams for nutrients, oxygen,
alkalinity and DIC. Overall, except for the carbonate system
and iron, the model performs quite well, as expected from the
comparison made in the previous section. The poorest agreement is found for both alkalinity and iron. For iron, the model
tends to strongly underestimate the spatial variability, both at
the surface and in the interior of the ocean. Through a reinspection of Fig. 8, we can see that this weak bias is not surprising. In particular, the gradients from the coastal regions
to the open ocean are generally too small. This suggests that
the sediment source of iron is too small and should either
be increased and/or made more variable. For the carbonate
system, the predicted spatial variability is overestimated, in
particular in the interior of the ocean. In fact, the data distribution which has been used to produce the observed climatology is rather coarse (Key et al., 2004). As a consequence,
the interpolation procedure strongly smooths the DIC and
alkalinity distribution. Thus, the GLODAP database probably underestimates the real variability of these tracers. To
avoid this problem, we should have used a non-interpolated
data product as for iron or mesozooplankton. To estimate the
potential uncertainty associated with the use of GLODAP,
we have used another alkalinity database only available at
the surface (Lee et al., 2006). The agreement between the
model and this database is much better (see Fig. 16), thus
confirming that interpolation in GLODAP potentially leads
to a strong underestimate of the real spatial variability.
Geosci. Model Dev., 8, 2465–2513, 2015
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O. Aumont et al.: A description of PISCES-v2
Figure 15. Taylor diagram of model–observation comparisons for
mesozooplankton using monthly mean fields. Data come from the
Green Ocean Project web site. Black dot corresponds to the global
ocean; red dot to the Atlantic Ocean, green dot to the Pacific Ocean,
brown dot to the Indian Ocean and gray dot to the Southern Ocean
(south of 45◦ S).
7
Sensitivity tests with some new parameterizations
A number of new parameterizations has been introduced in
the current version of PISCES. The objective of this section
is to briefly document the impact of some of these. To do so,
we have run a series of sensitivity experiments for a duration
of 10 years in which specific parameterizations have been either changed or removed. Table 7 summarizes the different
experiments performed. The objective of these tests is not
to unequivocally demonstrate that the new formulations improve the model skills but is rather to show the consequences
of their utilization on the model behavior.
7.1
Dependence of growth rate on light
In the first two experiments, PAR and LIGHT, the sensitivity
of the model results to the dependence of growth rate to light
has been tested. In the PAR experiment, PAR is set as a constant fraction of incident shortwave radiation, here 43 %, as
usually done in ocean biogeochemical models. Chlorophyll
distribution is almost identical to the standard simulation (not
shown). Furthermore, global primary production and export
production remain almost unchanged (see Table 7). Model
results are thus almost insensitive to the variability of the
fraction of shortwave radiation that is PAR. In the second
experiment, we use an alternative formulation of light limitation which corresponds to the standard parameterization as
proposed by Geider et al. (1997) (see Eq. 2b). In this formulation, the light saturation parameter Ek directly depends on
temperature and nutrient limitation. Thus, since the Q10 of
phytoplankton is close to 2, Ek is then predicted to be 6 to
8 times smaller in the very high latitudes than in the tropical
Geosci. Model Dev., 8, 2465–2513, 2015
Figure 16. Taylor diagrams of model–observation comparisons for
nutrients using monthly mean fields. The data are identical to those
used in previous plots. Panel (a) corresponds to the global ocean.
Panel (b) shows the comparison restricted to the top 100 m of the
ocean. Black dot corresponds to NO3 , brown dot to O2 , red dot to
PO4 , green dot to SiO3 , light-blue dot to DIC, purple dot to alkalinity and gray dot to iron. The additional purple dot labeled as AlkLee uses the database constructed by Lee et al. (2006) to compare
with the model.
domain. Furthermore, in the very oligotrophic regions, such
as the central subtropical gyres, Ek is close to 0 as a consequence of a very intense nutrient limitation. In the LIGHT
experiment, the initial slopes of P –I curves have been prescribed so that the resulting Ek are identical to those of the
standard case at 15 ◦ C for no nutrient limitation.
Figure 17a and b show the difference in chlorophyll between the LIGHT experiment and the standard case for two
seasons. The alternative parameterization of light limitation
produces changes in surface chlorophyll at both seasons. In
the very high latitudes of both hemispheres, surface chlorophyll is strongly increased during the corresponding growing season. The temperature dependence in the alternative
parameterization produces lower light saturation parameters
and thus, a weaker light limitation. On the contrary, in the
mid- to high latitudes of both hemispheres, surface chlorophyll is significantly lower, especially in the Southern Ocean
and in the Pacific Ocean. The temperature dependence of the
light saturation parameter results in a weaker light limitation during winter. As a consequence, chlorophyll concentrations and primary productivity are predicted to be higher
during this season generating a significant consumption and
export of nutrients. At the beginning of the growing season,
the stock of nutrients in the upper ocean is then lower which
leads to weaker and shorter spring blooms. In the very high
latitudes, the absence of light during winter and the presence of sea ice explain the different modeled response. In
the low latitudes, the differences are relatively small. Surface
chlorophyll concentrations tend to be higher in HNLC and
productive regions. The alternative formulation tends to produce a stronger light limitation in the subsurface and thus,
reduces the nutrient uptake below the surface. More iron
and macronutrients are advected into the surface layer (not
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Table 7. Sensitivity experiments performed with PISCES to evaluate the impact of specific parameterizations. Primary production (PP) and
export production at 150 m (EP) are in Gt C yr−1 .
Experiment
Description
Parameterization choices
PP
EP
PAR
LIGHT
SIZE
FOOD
Impact of variable PAR fraction
Impact of light limitation
Impact of variable cell sizes
Impact of food quality
ln_varpar = .false.
Eq. (2b)
xsizern, xsizerd = 1
θ N,I = 0.136
44.4
42.6
44.8
43.4
5.8
7.3
6.2
6.1
shown) which results in higher chlorophyll concentrations
and in some cases, in larger productive regions (for instance
in the tropical Atlantic Ocean and in the Arabian Sea).
Figure 18 shows the day at which blooms reach their maximum intensity in the Sea-Viewing Wide Field-of-View Senso
(SeaWiFS) data, in the standard case and in LIGHT. Over the
low and mid-latitudes as well as in the North Atlantic Ocean,
the timing of the bloom maximum predicted by the standard
model is in broad agreement with the satellite data. However,
in the central part of the subarctic gyre of the North Pacific,
the model simulates a bloom maximum which occurs much
too early in the growing season, in January compared to August in the satellite observations. A similar bias is also predicted in part of the Southern Ocean, especially in the eastern
part of the three sectors of this ocean. When the alternative
parameterization of light limitation is used, the bloom timing remains unchanged over most of the ocean, except in the
high latitudes in areas where the winter mixed layer remains
relatively shallow. Such a result is not surprising because the
alternative formulation predicts a much lower light saturation
parameter in cold waters which alleviates light limitation at
the beginning of the growing season. As a consequence, the
bloom occurs earlier in the growing season, which tends to
worsen the model behavior in the high latitudes of both hemispheres. In the North Pacific, the strong bias is not modified
by the alternative formulation which suggests that this bias
is not related to an incorrect description of light limitation.
In fact, the model predicts a very strong limitation of phytoplankton growth by iron during summer and thus, simulated
chlorophyll concentrations are very low. In winter, the mixed
layer deepens supplying the surface with iron. However, it remains relatively shallow preventing thus phytoplankton from
being severely light limited. Chlorophyll concentrations are
then maximum during winter and minimum during summer,
which is identical to what is observed in the subtropical
gyres, at BATS for instance (Lévy et al., 2005; Fernández I
et al., 2005). Yet, it is completely out of phase relative to
the observations, suggesting that in that region, the model either strongly overestimates iron limitation during summer or
that iron-light co-limitations are incorrectly parameterized in
PISCES.
The sensitivity experiment presented here shows that
model results are very sensitive to how light limitation is parameterized. Primary production, export production as well
www.geosci-model-dev.net/8/2465/2015/
as the magnitude of the bloom are strongly impacted by the
choice of the formulation describing light limitation of phytoplankton growth. The parameterization proposed by Geider
et al. (1997) shares some similarities with the Liebig’s law of
the minimum. When nutrients are very limiting, light limitation becomes negligible since Ek tends to 0. When light
is strongly limiting, nutrients limitation becomes unimportant and growth rate becomes linearly related to light and
Chl / C. The parameterization used in the standard case is
similar to the multiplicative description of the limiting factors. As a consequence, the standard parameterization predicts lower phytoplankton growth rates, smaller primary production and less intense blooms. On the other hand, the timing of the bloom maximum is much less sensitive to the formulation of light limitation, except in the strongly stratified
areas of the high latitudes. At low latitudes, light limitation at
the surface is of secondary importance, despite that light limitation in the subsurface appears to partly control the amount
of nutrients supplied to the surface. In the mid- and high latitudes, in areas characterized by deep winter mixed layers,
the timing of the bloom maximum (but not its magnitude)
appears to be virtually insensitive to the description of light
limitation. This means that other factors, such as the timing
of stratification, drive the timing of the bloom maximum.
7.2
Simple parameterization of cell size
In PISCES, a very basic parameterization of phytoplankton cell size has been developed to compute the values of
the half-saturation coefficients for the different nutrients (see
Eq. 7). This parameterization is based on the classical hypothesis, supported by observations, that the mean cell size
of a phytoplankton community increases as the biomass increases (e.g., Raimbault et al., 1988; Armstrong, 1994; Hurtt
and Armstrong, 1996). In the SIZE experiment, this simple
parameterization has been removed, i.e., the half-saturation
constants are kept constant to their minimum values as specified in Table 1.
Figure 17c and d display the differences in surface chlorophyll between the SIZE experiment and the standard configuration of the model. The largest differences are simulated in
the high latitudes of both hemispheres, during the growing
season. A closer inspection of the model results show that
the largest changes occur at the end of the spring or summer
bloom, when the exhaustion in nutrients becomes a major
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Figure 17. Surface seasonal mean chlorophyll anomaly (mg chl a m−3 ) relative to the standard simulation in April-May-June (left column)
and November-December-January (right column). Panels (a) and (b) correspond to the LIGHT test; panels (c) and (d) show to the SIZE test;
panels (e) and (f) display the FOOD test.
limiting factor. In the standard experiment, the cell-size parameterization produces high half-saturation constants during the phytoplankton bloom since they directly depend on
the biomass level. Thus, nutrient limitation occurs earlier and
is more severe leading to a shorter and less intense bloom. In
the eastern boundary upwelling systems, the biomass is also
very high. However, unlike in the high latitudes, the phyto-
Geosci. Model Dev., 8, 2465–2513, 2015
plankton biomass is mainly controlled by grazing so that nutrient concentrations are generally much higher than the values of the high saturation constants. In the subtropical oligotrophic gyres, the impact is negligible since the mean cell
size is predicted to be at its minimal value in the standard experiment, which is equivalent to what is imposed in the SIZE
experiment.
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O. Aumont et al.: A description of PISCES-v2
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7.3
Figure 18. Day of the year at which sea surface chlorophyll is maximum. Panel (a) corresponds to the observations; panel (b) displays
the standard simulation. Panel (c) shows the difference between
the LIGHT and the standard experiments. Only the regions where
the amplitude of the seasonal cycle exceeds 0.1 mg chl a m−3 are
shown.
The impact of the cell-size parameterization on nutrients is
small, except for silicate in the equatorial Pacific Ocean (not
shown). In this region, nanophytoplankton become strongly
favored in the SIZE experiment because in the standard case,
their cell size is not predicted to be minimum, whereas this
is the case for diatoms. When the cell-size parameterization is removed, nanophytoplankton biomass increases and
completely out compete diatoms. As a consequence, silicate
consumption in the equatorial Pacific Ocean is strongly reduced which explains the simulated higher values in the SIZE
experiment. However, the total chlorophyll concentration is
nearly identical because the decrease in diatoms compensates
for the increase in nanophytoplankton. Furthermore, the total chlorophyll biomass is regulated by the total supply in
iron, whereas the contribution of the different phytoplankton
species is driven by their competitive abilities (here specified
by the values of their half-saturation constants).
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Food quality and grazing
Food quality may have profound impacts on the grazing activity by zooplankton as discussed by Mitra et al. (2007).
When absorbing prey with poor nutritional value, zooplankton may have two different options: (1) increase the retention time of the prey to extract as many metabolites as they
can (Plath and Boersma, 2001), or (2) decrease the retention
time of the preys to maintain the highest possible metabolite
concentration in the digestive apparatus and thus to increase
the probability to absorb valuable compounds (Tirelli and
Mayzaud, 2005; Dutz et al., 2008). In the first case, growth
efficiency is increased whereas it is decreased in the second case. In PISCES, poor food quality is assumed to impair
gross growth efficiency (eZ ) of both microzooplankton and
mesozooplankton based on the stoichiometric ratios of their
preys (Fe / C and N / C, see Eq. 27). In the FOOD sensitivity experiment, the effect of food quality on the gross growth
Z is set to 1.
efficiency has been removed, i.e., eN
Surface chlorophyll concentrations are almost unaltered
when the impact of food quality is removed (see Fig. 17e and
f). The only noticeable differences are simulated from the
equatorial Pacific Ocean where very strong iron limitation
causes very low Fe / C ratios in phytoplankton. In the FOOD
experiment, these low Fe / C ratios do not reduce zooplankton growth efficiency. Grazing pressure on phytoplankton is
then higher. The nutrients distributions are also very close to
those predicted in the standard experiment. Thus, food quality appears to have minimal consequences on chlorophyll and
nutrients, at least in terms of their absolute values.
Figure 19 shows the relative changes in phytoplankton,
microzooplankton and mesozooplankton biomasses (in carbon). A significant reduction in the carbon biomass of phytoplankton is predicted in the FOOD experiment. This reduction is maximum in the subtropical gyres where it may exceed 40 % because of more intense grazing by zooplankton.
These changes are not perceptible in chlorophyll concentrations (at least with the color scale chosen on Fig. 17) because
of the extremely low Chl / C in the gyres. Both on microzooplankton and mesozooplankton, the differences between
the FOOD and the standard experiments are even more pronounced. Both zooplankton biomasses increase by more than
100 % in the subtropical gyres of all oceans and this increase
even exceeds 200 % in the subtropical gyre of the South Pacific Ocean.
Food quality may thus have very important impacts on
zooplankton, especially in the very oligotrophic regions. Furthermore, the importance of food quality is predicted to be
more critical in regions depleted in nitrogen, characterized
by very low N / C ratios in phytoplankton, than in iron limited areas. Several points may explain this greater sensitivity. First, even in the most severely iron limited areas, the
Fe / C ratio in phytoplankton drops very rarely below half
the value of the Fe / C ratio in zooplankton. In the central
part of the subtropical gyres, where nitrogen limitation is the
Geosci. Model Dev., 8, 2465–2513, 2015
2500
Figure 19. Annual-mean relative change in the surface carbon
biomass of total phytoplankton (panel a), microzooplankton (panel
b), and mesozooplankton (panel c) in the FOOD experiment compared to the standard case.
most intense, N / C ratios in phytoplankton can reach 0.04,
that is about 3 times less than the N / C ratio of zooplankton. Second, the available food in the intense oligotrophic
areas is much lower than in the iron limited regions. Chlorophyll concentrations in the typical HNLC regions are generally around 0.2 to 0.3 mg chl a m−3 , whereas it is below
0.1 mg chl a m−3 in the subtropical gyres. As a consequence,
zooplankton biomass is lower in the subtropical gyres which
increases the magnitude of the relative changes.
8
Conclusions
In this paper, we have presented a full and thorough description of the current state of the ocean biogeochemical model
PISCES, called PISCES-v2. Since the latest published version of the model (Aumont and Bopp, 2006), PISCES-v2 has
undergone major changes both in terms of the modeled processes and of the model structure and performance. Relative
to its previous version PISCES-v1, key changes are a maGeosci. Model Dev., 8, 2465–2513, 2015
O. Aumont et al.: A description of PISCES-v2
jor redesign of phytoplankton growth description, including
a quota-based representation of iron limitation, an improvement of the zooplankton compartment, a better description
of the benthic processes and a simple description of nitrogen fixation by diazotrophs. A complete list of the changes
made in PISCES-v2 relative to its previously published version is detailed in Sect. 2. The performance of the model has
been then evaluated using a climatological simulation run to
quasi-steady state. The model produces reasonable surface
distributions of chlorophyll, mesozooplankton and nutrients
(including iron) and simulates consistent vertical distributions of the main biogeochemical tracers. Some of the main
deficiencies of the model are the spatial distribution of the
oxygen minimum zones, the silicic acid distribution in the
Southern Ocean, too elevated nutrients concentrations in the
deep Atlantic Ocean and an out-of-phase predicted seasonal
cycle of chlorophyll in the subarctic Pacific Ocean.
PISCES includes several optional parameterizations that
may be activated from the namelist. In this study, we have
presented the impacts of some of these optional formulations
evaluated in a set of sensitivity experiments. The choice of
the light limitation scheme has the largest effect on the model
solution, especially on chlorophyll. The amplitude of the
seasonal cycle in the high latitudes is profoundly impacted
whereas the timing of the bloom maximum is in general only
very moderately altered. The effect of food quality on the
growth efficiency of zooplankton has been shown to lead
to important relative changes in the oligotrophic subtropical
gyres. The model suggests that it is critical to maintain sufficiently high chlorophyll levels in these regions. It may also
contribute to, at least partly, explaining the too low primary
productivity simulated by other biogeochemical models in
the subtropical gyres (Yool et al., 2013).
The description of PISCES presented here has been restricted to the core scheme which can be obtained online
from different SVN repositories depending on the dynamical framework in which it is embedded (see the Introduction
for a list of theses repositories). In addition to the description
of the lower trophic levels of marine ecosystems, and the biogeochemical cycles of carbon and of the main nutrients (N,
P, Si, Fe), as described in this manuscript, a few additional
modules have been embedded into PISCES. These modules
enable the model to compute the cycles of climate-relevant
gases emitted by the ocean such as dimethylsulfide (DMS)
(Bopp et al., 2008), and nitrous oxide (N2 O) (Martinez-Rey
et al., 2015). An explicit representation of paleo-proxies,
such as δ 13 C (Tagliabue et al., 2009b), Pa / Th (Dutay et al.,
2009), Nd (Arsouze et al., 2009), is also available.
PISCES is still in a phase of active development despite
the fact that its development started more than 10 years ago.
Avenues for future improvements are large and numerous
and concern all aspects of the model. The challenges confronting marine biogeochemical modeling have been identified in many dedicated studies (e.g., Doney, 1999; Hood
et al., 2006; Merico et al., 2009; Smith et al., 2011; Mitra
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O. Aumont et al.: A description of PISCES-v2
et al., 2014). Setting priorities in a long list of potential necessary modifications is a rather difficult task which relies not
only on the diagnostic of the major deficiencies of the current
model but also on the future research scope envisioned for
the model. In the coming years, PISCES will evolve along
two main avenues. First, a more sophisticated treatment of
phytoplankton physiology will replace the current relatively
simple scheme. A main consequence is the representation of
variable elemental ratios for all major elements (N, P, Fe,
Si, C). Redfield–Monod models have been shown to exhibit
serious deficiencies which advocate for their replacement
by more detailed mechanistic schemes (Flynn, 2010; Smith
et al., 2011). Second, almost all marine biogeochemical mod-
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2501
els have been built on the classical distinction between phytoplanktonic autotrophic organisms and zooplanktonic heterotrophic organisms. However, this dichotomy has been increasingly challenged in the recent years as observations
have shown that most protists, probably with the exception
of diatoms, have to a lesser or greater degree a mixotrophic
status (e.g., Stoecker, 1998; Flynn et al., 2013). The conceptual schemes on which biogeochemical models, including
PISCES, should then be revised, in particular the distinction
between phytoplankton and microzooplankton.
Geosci. Model Dev., 8, 2465–2513, 2015
2502
Appendix A: Model structure
The model is being coded in FORTRAN 90. To activate
PISCES, the cpp key key_pisces should be declared.
Only the subroutines that compute the biological or chemical
sources and sinks are considered to be part of PISCES. Thus,
this excludes the computation of the advection–diffusion
equation (the transport of the tracers), as it is not specific to
PISCES. There are two types of subroutines: the initialization of the tracers and of the parameters and the computation
of the various biogeochemical sources and sinks. The latter
PISCES subroutines are called from within the ocean model
time loop.
The objective here is not to precisely detail the PISCES
code but rather to list the different modules and to briefly
describe their role. All the subroutines that compute the biogeochemical sources/sinks are called from p4zsms which is
then the main PISCES subroutine.
– p4zbio.F90: computation of the new tracer concentrations by summing up all the different sources and sinks;
O. Aumont et al.: A description of PISCES-v2
– p4zsink.F90: aggregation of organic matter, computation of the particles sinking speeds. Vertical sedimentation of particles using a MUSCL advection scheme;
– p4zsms.F90: main PISCES subroutine which calls the
other subroutine.
Besides the subroutines listed above, several subroutines
perform the model initialization. We will only discuss the
initialization of the parameters necessary to PISCES. The
tracers concentrations are excluded here as their initialization will of course vary with the ocean model.
– trcini.pisces.F90: initialization of various biogeochemical parameters. Allocation of the arrays used in PISCES.
This subroutine also calls all the initialization subroutines included in the PISCES subroutines listed above.
– trcnam_pisces.F90: this subroutine reads the information necessary to write the netcdf files when IOM is not
used.
– p4zche.F90: computation of the various chemical constants;
– par_pisces.F90: it sets the PISCES parameters such as
the number of tracers and the name of the indices, the
number of additional diagnostics, etc.
– p4zfechem.F90: computation of the iron chemistry.
Scavenging of iron, aggregation of iron colloids;
– sms_pisces.F90: this subroutine defines some general
PISCES variables and arrays and allocates them.
– p4zflx.F90: air–sea fluxes of CO2 and O2 ;
– p4zint.F90: time interpolation of various terms (e.g.,
growth rate);
Many parameter values of the model can be specified from
the namelist namelist_pisces. When such is the case,
the corresponding parameter name in the namelist file is indicated in Table A1a–d.
– p4zlim.F90: co-limitations of phytoplankton growth by
the different nutrients;
– p4zlys.F90: calcite chemistry and dissolution;
– p4zmeso.F90: sources and sinks of mesozooplankton
(mortality, grazing, etc.);
– p4zmicro.F90: sources and sinks of microzooplankton;
– p4zmort.F90: computation of the various mortality
terms of nanophytoplankton and diatoms;
– p4zopt.F90: optical model and computation of the euphotic depth;
– p4zprod.F90: growth rate of the two phytoplankton
groups;
– p4zrem.F90: remineralization of organic matter, dissolution of biogenic silica;
– p4zsed.F90: top and bottom boundary conditions of the
biogeochemical tracers (deposition, sedimentary losses,
etc.);
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O. Aumont et al.: A description of PISCES-v2
Table A1. (a) Model parameters for phytoplankton with their default values in PISCES. (b) Model parameters for zooplankton
with their default values in PISCES. (c) Model parameters for organic and inorganic matter with their default values in PISCES. (d)
Model parameters for various processes with their default values in
PISCES.
2503
Table A1. Continued.
(c)
(a)
Parameter
Coding name
bresp
αI
δI
I,min
KNH
bresp
pislope; pislope2
excret; excret2
concnnh4; concdnh4
4
I,min
KNO
3
1
KSi
2
KSi
I,min
KFe
I
Srat
Si,D
θm
Fe,I
θopt
Fe,I
θmax
mI
wP
D
wmax
Km
Chl,I
θmax
Chl
θmin
Imax
concnno3; concdno3
xksi1
xksi2
concnfer; concdfer
xsizern; xsizerd
grosip
qnfelim; qdfelim
fecnm; fecdm
mprat; mprat2
wchl
wchld
xkmort
chlcnm; chlcdm
chlcmin
xsizephy; xsizedia
Parameter
Coding name
λDOC
KDOC
Bact
KNO
3
Bact
KNH
4
Bact
KFe
λPOC
wPOC
min
wGOC
wdust
λFe
λdust
Fe
λCaCO3
nca
0
χlab
slow
λPSi
λfast
PSi
xremik
xkdoc
concbno3
concbnh4
concbfe
xremip
wsbio
wsbio2
wdust
xlam1
xlamdust
kdca
nca
xsilab
xsirem
xsiremlab
Table A1. Continued.
Table A1. Continued.
(b)
Parameter
Coding name
(d)
I
emax
σI
epsher; epsher2
unass; unass2
sigma; sigma2
graze; graze2
grazflux
xkgraz; xkgraz2
xpref2p; xprefp
xpref2d; xprefc
xpref2c; xprefpoc
xprefz
xthresh; xthresh2
mzrat; mzrat2
resrat; resrat2
part; part2
ferat3
Parameter
Coding name
λNH4
O2 min,1
LT
m
Nfix
Dz
KFe
Efix
Feice
sed
FFe,min
SolFe
rCaCO3
nitrif
oxymin
ligand
nitrfix
concfediaz
diazolight
icefeinput
sedfeinput
dustsolub
caco3r
γI
I
gm
M
gFF
I
KG
I
pP
I
pD
I
pPOC
M
pZ
I
Fthresh
mI
rI
νI
θ Fe,Zoo
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Geosci. Model Dev., 8, 2465–2513, 2015
2504
Acknowledgements. The authors are grateful to the whole community of PISCES users. The model would be useless without them.
In particular, we thank Thomas Gorguès, Keith B. Rodgers,
Coralie Perruche, Christophe Menkès, Vincent Echevin,
Gildas Cambon and the whole NEMO system team for their
precious help, expertise and support which made the release of this
version possible. O. Aumont, L. Bopp, M. Gehlen were supported
by ANR-CEP09 MACROES. O. Aumont received additional
support from the Labex Mer via grant ANR-10-LABX-19-01.
Olivier Aumont will be eternally grateful to Ernst Maier-Reimer.
Even if he did not directly participate in the design of PISCES,
nothing would have been possible without him. PISCES was built
upon HAMOCC3 and HAMOCC3.1 and still some parts of the
current code of PISCES come from these models. This work is
dedicated to his memory.
Edited by: A. Ridgwell
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